Large degree polynomial function [on hold]Solve a polynomial of degree dHow come the Bernstein operator...
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Large degree polynomial function [on hold]
Solve a polynomial of degree dHow come the Bernstein operator creates a polynomial of the same degree as its input function?Third degree polynomial with integer coefficient and three irrational rootsfactorization of even degree polynomialPolynomial of $11^{th}$ degreeTrigonometric Roots of a PolynomialZeros of a Fourth Degree PolynomialHow to determine if a polynomial is bounded from below?A question about a self-reciprocal polynomial of even degreeHow to solve equation with exponents multiplied with a polynomial?
0
$begingroup$
How does one solve for $x$ in a polynomial of the form
$ax^{n} + bx^{left(n - 1right)} + c = 0$, given that $n$ is a larger number ?. For example:
$displaystyle x^{100} - 3x^{99} + 1 = 0$
polynomials
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
asked Mar 9 at 17:51
UNIBONUNIBON
52
$endgroup$
put on hold as off-topic by Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh Mar 10 at 2:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
0
$begingroup$
How does one solve for $x$ in a polynomial of the form
$ax^{n} + bx^{left(n - 1right)} + c = 0$, given that $n$ is a larger number ?. For example:
$displaystyle x^{100} - 3x^{99} + 1 = 0$
polynomials
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
asked Mar 9 at 17:51
UNIBONUNIBON
52
$endgroup$
put on hold as off-topic by Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh Mar 10 at 2:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
Welcome to MSE. Please give more context to this question, so people can give you appropriate answers. Is there a specific polynomial you are interested in? Are you looking for exact solutions or numerical ones? Are you only interested in real solutions, or do you want the complex ones, too? What have you tried?
$endgroup$
– saulspatz
Mar 9 at 17:57
$begingroup$
For example: x^100-3x^99+1=0. I need both real and complex solutions.
$endgroup$
– UNIBON
Mar 9 at 18:03
$begingroup$
Please add the context to the body of your question. Many people browsing questions will vote to close a question with no more context than this, without looking at the comments. Also, you ought to use MathJax to make your posts more readable. Look at how I edited the question.
$endgroup$
– saulspatz
Mar 9 at 18:11
$begingroup$
Thanks...I have tried downloading the mathjax but it wasn't successful.
$endgroup$
– UNIBON
Mar 9 at 18:22
1
$begingroup$
You don't need to download MathJax. You just put formatting commands in the text. For example$x^{100}-3x^{99}+1=0$is displayed as $x^{100}-3x^{99}+1=0$
$endgroup$
– saulspatz
Mar 9 at 18:24
add a comment |
0
0
0
$begingroup$
How does one solve for $x$ in a polynomial of the form
$ax^{n} + bx^{left(n - 1right)} + c = 0$, given that $n$ is a larger number ?. For example:
$displaystyle x^{100} - 3x^{99} + 1 = 0$
polynomials
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
asked Mar 9 at 17:51
UNIBONUNIBON
52
$endgroup$
How does one solve for $x$ in a polynomial of the form
$ax^{n} + bx^{left(n - 1right)} + c = 0$, given that $n$ is a larger number ?. For example:
$displaystyle x^{100} - 3x^{99} + 1 = 0$
polynomials
polynomials
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
asked Mar 9 at 17:51
UNIBONUNIBON
52
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
asked Mar 9 at 17:51
UNIBONUNIBON
52
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
edited Mar 9 at 18:29
Felix Marin
68.4k7109144
68.4k7109144
asked Mar 9 at 17:51
UNIBONUNIBON
52
asked Mar 9 at 17:51
UNIBONUNIBON
52
asked Mar 9 at 17:51
UNIBONUNIBON
52
52
put on hold as off-topic by Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh Mar 10 at 2:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh Mar 10 at 2:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Servaes, Travis, Eevee Trainer, Alex Provost, Shailesh
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
Welcome to MSE. Please give more context to this question, so people can give you appropriate answers. Is there a specific polynomial you are interested in? Are you looking for exact solutions or numerical ones? Are you only interested in real solutions, or do you want the complex ones, too? What have you tried?
$endgroup$
– saulspatz
Mar 9 at 17:57
$begingroup$
For example: x^100-3x^99+1=0. I need both real and complex solutions.
$endgroup$
– UNIBON
Mar 9 at 18:03
$begingroup$
Please add the context to the body of your question. Many people browsing questions will vote to close a question with no more context than this, without looking at the comments. Also, you ought to use MathJax to make your posts more readable. Look at how I edited the question.
$endgroup$
– saulspatz
Mar 9 at 18:11
$begingroup$
Thanks...I have tried downloading the mathjax but it wasn't successful.
$endgroup$
– UNIBON
Mar 9 at 18:22
1
$begingroup$
You don't need to download MathJax. You just put formatting commands in the text. For example$x^{100}-3x^{99}+1=0$is displayed as $x^{100}-3x^{99}+1=0$
$endgroup$
– saulspatz
Mar 9 at 18:24
add a comment |
1
$begingroup$
Welcome to MSE. Please give more context to this question, so people can give you appropriate answers. Is there a specific polynomial you are interested in? Are you looking for exact solutions or numerical ones? Are you only interested in real solutions, or do you want the complex ones, too? What have you tried?
$endgroup$
– saulspatz
Mar 9 at 17:57
$begingroup$
For example: x^100-3x^99+1=0. I need both real and complex solutions.
$endgroup$
– UNIBON
Mar 9 at 18:03
$begingroup$
Please add the context to the body of your question. Many people browsing questions will vote to close a question with no more context than this, without looking at the comments. Also, you ought to use MathJax to make your posts more readable. Look at how I edited the question.
$endgroup$
– saulspatz
Mar 9 at 18:11
$begingroup$
Thanks...I have tried downloading the mathjax but it wasn't successful.
$endgroup$
– UNIBON
Mar 9 at 18:22
1
$begingroup$
You don't need to download MathJax. You just put formatting commands in the text. For example$x^{100}-3x^{99}+1=0$is displayed as $x^{100}-3x^{99}+1=0$
$endgroup$
– saulspatz
Mar 9 at 18:24
1
1
$begingroup$
Welcome to MSE. Please give more context to this question, so people can give you appropriate answers. Is there a specific polynomial you are interested in? Are you looking for exact solutions or numerical ones? Are you only interested in real solutions, or do you want the complex ones, too? What have you tried?
$endgroup$
– saulspatz
Mar 9 at 17:57
$begingroup$
Welcome to MSE. Please give more context to this question, so people can give you appropriate answers. Is there a specific polynomial you are interested in? Are you looking for exact solutions or numerical ones? Are you only interested in real solutions, or do you want the complex ones, too? What have you tried?
$endgroup$
– saulspatz
Mar 9 at 17:57
$begingroup$
For example: x^100-3x^99+1=0. I need both real and complex solutions.
$endgroup$
– UNIBON
Mar 9 at 18:03
$begingroup$
For example: x^100-3x^99+1=0. I need both real and complex solutions.
$endgroup$
– UNIBON
Mar 9 at 18:03
$begingroup$
Please add the context to the body of your question. Many people browsing questions will vote to close a question with no more context than this, without looking at the comments. Also, you ought to use MathJax to make your posts more readable. Look at how I edited the question.
$endgroup$
– saulspatz
Mar 9 at 18:11
$begingroup$
Please add the context to the body of your question. Many people browsing questions will vote to close a question with no more context than this, without looking at the comments. Also, you ought to use MathJax to make your posts more readable. Look at how I edited the question.
$endgroup$
– saulspatz
Mar 9 at 18:11
$begingroup$
Thanks...I have tried downloading the mathjax but it wasn't successful.
$endgroup$
– UNIBON
Mar 9 at 18:22
$begingroup$
Thanks...I have tried downloading the mathjax but it wasn't successful.
$endgroup$
– UNIBON
Mar 9 at 18:22
1
1
$begingroup$
You don't need to download MathJax. You just put formatting commands in the text. For example
$x^{100}-3x^{99}+1=0$ is displayed as $x^{100}-3x^{99}+1=0$$endgroup$
– saulspatz
Mar 9 at 18:24
$begingroup$
You don't need to download MathJax. You just put formatting commands in the text. For example
$x^{100}-3x^{99}+1=0$ is displayed as $x^{100}-3x^{99}+1=0$$endgroup$
– saulspatz
Mar 9 at 18:24
add a comment |
1 Answer
1
active
oldest
votes
-1
$begingroup$
I'm still not sure I understand the question, but this is easy with a computer, assuming you want numerical values. I wrote a python script to do this. (Annoyingly, numpy expects the leading coefficient $x^k$ of a polynomial of degre $n$ to be at index $n-k.$)
import numpy as np
p = np.zeros((101))
p[0]=1
p[1]=-3
p[100]=1
roots = np.roots(p)
for idx, root in enumerate(roots):
print(idx, root)
produces this output instantaneously:
0 (3.000000000000001+0j)
1 (-0.7364491456451218+0.6565561896636651j)
2 (-0.7364491456451218-0.6565561896636651j)
3 (-0.7764559201902995+0.6085861156452325j)
4 (-0.7764559201902995-0.6085861156452325j)
5 (-0.8133485650308432+0.5581912452828626j)
6 (-0.8133485650308432-0.5581912452828626j)
7 (-0.6934865839515425+0.701909773950447j)
8 (-0.6934865839515425-0.701909773950447j)
9 (-0.8469810844038753+0.5055727935082724j)
10 (-0.8469810844038753-0.5055727935082724j)
11 (-0.8772204006792861+0.4509407077743689j)
12 (-0.8772204006792861-0.4509407077743689j)
13 (-0.647738305184038+0.7444654479736014j)
14 (-0.647738305184038-0.7444654479736014j)
15 (-0.9039468754197537+0.39451284443370066j)
16 (-0.9039468754197537-0.39451284443370066j)
17 (-0.5993854422724829+0.7840527747018899j)
18 (-0.5993854422724829-0.7840527747018899j)
19 (-0.9270547780297581+0.3365141137728261j)
20 (-0.9270547780297581-0.3365141137728261j)
21 (-0.548619483695713+0.8205129677981756j)
22 (-0.548619483695713-0.8205129677981756j)
23 (-0.9464527000806124+0.2771755970853744j)
24 (-0.9464527000806124-0.2771755970853744j)
25 (-0.4956415264634955+0.8536995127614468j)
26 (-0.4956415264634955-0.8536995127614468j)
27 (-0.4406614924968664+0.8834787396172576j)
28 (-0.4406614924968664-0.8834787396172576j)
29 (-0.9620639136235793+0.21673363928004163j)
30 (-0.9620639136235793-0.21673363928004163j)
31 (-0.38389731168552527+0.909730344970996j)
32 (-0.38389731168552527-0.909730344970996j)
33 (-0.3255740750583158+0.9323478614682946j)
34 (-0.3255740750583158-0.9323478614682946j)
35 (0.7577303192949743+0.6394431221673114j)
36 (0.7577303192949743-0.6394431221673114j)
37 (0.7970347431023204+0.590099961131214j)
38 (0.7970347431023204-0.590099961131214j)
39 (0.7153872255455767+0.6861568685320916j)
40 (0.7153872255455767-0.6861568685320916j)
41 (0.8331341618753201+0.5383229631320452j)
42 (0.8331341618753201-0.5383229631320452j)
43 (0.6701830619131026+0.7300572029385581j)
44 (0.6701830619131026-0.7300572029385581j)
45 (0.8658742980131764+0.48431875063231544j)
46 (0.8658742980131764-0.48431875063231544j)
47 (0.6223059154766839+0.7709722084480215j)
48 (0.6223059154766839-0.7709722084480215j)
49 (0.5719535879849889+0.8087425205066434j)
50 (0.5719535879849889-0.8087425205066434j)
51 (0.8951137460294047+0.4283044061929457j)
52 (0.8951137460294047-0.4283044061929457j)
53 (0.5193328204049903+0.8432217744454027j)
54 (0.5193328204049903-0.8432217744454027j)
55 (0.9207248128533412+0.3705068199042141j)
56 (0.9207248128533412-0.3705068199042141j)
57 (0.46465850700695943+0.8742770284347632j)
58 (0.46465850700695943-0.8742770284347632j)
59 (0.9425943804458727+0.31116194515065604j)
60 (0.9425943804458727-0.31116194515065604j)
61 (-0.2659231616491491+0.9512390729535296j)
62 (-0.2659231616491491-0.9512390729535296j)
63 (0.4081528934442288+0.9017891596220862j)
64 (0.4081528934442288-0.9017891596220862j)
65 (0.9606247774115534+0.2505139365561644j)
66 (0.9606247774115534-0.2505139365561644j)
67 (0.9747346342048573+0.1888141457593689j)
68 (0.9747346342048573-0.1888141457593689j)
69 (0.35004475520869627+0.9256532298451866j)
70 (0.35004475520869627-0.9256532298451866j)
71 (-0.20518134277364738+0.966326373881672j)
72 (-0.20518134277364738-0.966326373881672j)
73 (0.2905685546336416+0.9457788166930109j)
74 (0.2905685546336416-0.9457788166930109j)
75 (0.9848596842823707+0.1263199581194814j)
76 (0.9848596842823707-0.1263199581194814j)
77 (-0.9738266720335937+0.15542892061869676j)
78 (-0.9738266720335937-0.15542892061869676j)
79 (0.2299635761582389+0.9620903055655939j)
80 (0.2299635761582389-0.9620903055655939j)
81 (-0.14358986755051278+0.977547071822796j)
82 (-0.14358986755051278-0.977547071822796j)
83 (0.1684730408262214+0.9745271385958778j)
84 (0.1684730408262214-0.9745271385958778j)
85 (0.9909534640600726+0.06329346693748208j)
86 (0.9909534640600726-0.06329346693748208j)
87 (0.9929878610066416+0j)
88 (-0.9816944521616785+0.09350551126383294j)
89 (-0.9816944521616785-0.09350551126383294j)
90 (0.10634320197349573+0.9830440167028471j)
91 (0.10634320197349573-0.9830440167028471j)
92 (-0.08139353360287407+0.9848536322040496j)
93 (-0.08139353360287407-0.9848536322040496j)
94 (0.043822424798379056+0.987611051554128j)
95 (0.043822424798379056-0.987611051554128j)
96 (-0.01883974695583218+0.9882138647642805j)
97 (-0.01883974695583218-0.9882138647642805j)
98 (-0.9856361368133812+0.031209912383584327j)
99 (-0.9856361368133812-0.031209912383584327j)
Is there some reason that this isn't good enough?
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
-1
$begingroup$
I'm still not sure I understand the question, but this is easy with a computer, assuming you want numerical values. I wrote a python script to do this. (Annoyingly, numpy expects the leading coefficient $x^k$ of a polynomial of degre $n$ to be at index $n-k.$)
import numpy as np
p = np.zeros((101))
p[0]=1
p[1]=-3
p[100]=1
roots = np.roots(p)
for idx, root in enumerate(roots):
print(idx, root)
produces this output instantaneously:
0 (3.000000000000001+0j)
1 (-0.7364491456451218+0.6565561896636651j)
2 (-0.7364491456451218-0.6565561896636651j)
3 (-0.7764559201902995+0.6085861156452325j)
4 (-0.7764559201902995-0.6085861156452325j)
5 (-0.8133485650308432+0.5581912452828626j)
6 (-0.8133485650308432-0.5581912452828626j)
7 (-0.6934865839515425+0.701909773950447j)
8 (-0.6934865839515425-0.701909773950447j)
9 (-0.8469810844038753+0.5055727935082724j)
10 (-0.8469810844038753-0.5055727935082724j)
11 (-0.8772204006792861+0.4509407077743689j)
12 (-0.8772204006792861-0.4509407077743689j)
13 (-0.647738305184038+0.7444654479736014j)
14 (-0.647738305184038-0.7444654479736014j)
15 (-0.9039468754197537+0.39451284443370066j)
16 (-0.9039468754197537-0.39451284443370066j)
17 (-0.5993854422724829+0.7840527747018899j)
18 (-0.5993854422724829-0.7840527747018899j)
19 (-0.9270547780297581+0.3365141137728261j)
20 (-0.9270547780297581-0.3365141137728261j)
21 (-0.548619483695713+0.8205129677981756j)
22 (-0.548619483695713-0.8205129677981756j)
23 (-0.9464527000806124+0.2771755970853744j)
24 (-0.9464527000806124-0.2771755970853744j)
25 (-0.4956415264634955+0.8536995127614468j)
26 (-0.4956415264634955-0.8536995127614468j)
27 (-0.4406614924968664+0.8834787396172576j)
28 (-0.4406614924968664-0.8834787396172576j)
29 (-0.9620639136235793+0.21673363928004163j)
30 (-0.9620639136235793-0.21673363928004163j)
31 (-0.38389731168552527+0.909730344970996j)
32 (-0.38389731168552527-0.909730344970996j)
33 (-0.3255740750583158+0.9323478614682946j)
34 (-0.3255740750583158-0.9323478614682946j)
35 (0.7577303192949743+0.6394431221673114j)
36 (0.7577303192949743-0.6394431221673114j)
37 (0.7970347431023204+0.590099961131214j)
38 (0.7970347431023204-0.590099961131214j)
39 (0.7153872255455767+0.6861568685320916j)
40 (0.7153872255455767-0.6861568685320916j)
41 (0.8331341618753201+0.5383229631320452j)
42 (0.8331341618753201-0.5383229631320452j)
43 (0.6701830619131026+0.7300572029385581j)
44 (0.6701830619131026-0.7300572029385581j)
45 (0.8658742980131764+0.48431875063231544j)
46 (0.8658742980131764-0.48431875063231544j)
47 (0.6223059154766839+0.7709722084480215j)
48 (0.6223059154766839-0.7709722084480215j)
49 (0.5719535879849889+0.8087425205066434j)
50 (0.5719535879849889-0.8087425205066434j)
51 (0.8951137460294047+0.4283044061929457j)
52 (0.8951137460294047-0.4283044061929457j)
53 (0.5193328204049903+0.8432217744454027j)
54 (0.5193328204049903-0.8432217744454027j)
55 (0.9207248128533412+0.3705068199042141j)
56 (0.9207248128533412-0.3705068199042141j)
57 (0.46465850700695943+0.8742770284347632j)
58 (0.46465850700695943-0.8742770284347632j)
59 (0.9425943804458727+0.31116194515065604j)
60 (0.9425943804458727-0.31116194515065604j)
61 (-0.2659231616491491+0.9512390729535296j)
62 (-0.2659231616491491-0.9512390729535296j)
63 (0.4081528934442288+0.9017891596220862j)
64 (0.4081528934442288-0.9017891596220862j)
65 (0.9606247774115534+0.2505139365561644j)
66 (0.9606247774115534-0.2505139365561644j)
67 (0.9747346342048573+0.1888141457593689j)
68 (0.9747346342048573-0.1888141457593689j)
69 (0.35004475520869627+0.9256532298451866j)
70 (0.35004475520869627-0.9256532298451866j)
71 (-0.20518134277364738+0.966326373881672j)
72 (-0.20518134277364738-0.966326373881672j)
73 (0.2905685546336416+0.9457788166930109j)
74 (0.2905685546336416-0.9457788166930109j)
75 (0.9848596842823707+0.1263199581194814j)
76 (0.9848596842823707-0.1263199581194814j)
77 (-0.9738266720335937+0.15542892061869676j)
78 (-0.9738266720335937-0.15542892061869676j)
79 (0.2299635761582389+0.9620903055655939j)
80 (0.2299635761582389-0.9620903055655939j)
81 (-0.14358986755051278+0.977547071822796j)
82 (-0.14358986755051278-0.977547071822796j)
83 (0.1684730408262214+0.9745271385958778j)
84 (0.1684730408262214-0.9745271385958778j)
85 (0.9909534640600726+0.06329346693748208j)
86 (0.9909534640600726-0.06329346693748208j)
87 (0.9929878610066416+0j)
88 (-0.9816944521616785+0.09350551126383294j)
89 (-0.9816944521616785-0.09350551126383294j)
90 (0.10634320197349573+0.9830440167028471j)
91 (0.10634320197349573-0.9830440167028471j)
92 (-0.08139353360287407+0.9848536322040496j)
93 (-0.08139353360287407-0.9848536322040496j)
94 (0.043822424798379056+0.987611051554128j)
95 (0.043822424798379056-0.987611051554128j)
96 (-0.01883974695583218+0.9882138647642805j)
97 (-0.01883974695583218-0.9882138647642805j)
98 (-0.9856361368133812+0.031209912383584327j)
99 (-0.9856361368133812-0.031209912383584327j)
Is there some reason that this isn't good enough?
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
$endgroup$
add a comment |
-1
$begingroup$
I'm still not sure I understand the question, but this is easy with a computer, assuming you want numerical values. I wrote a python script to do this. (Annoyingly, numpy expects the leading coefficient $x^k$ of a polynomial of degre $n$ to be at index $n-k.$)
import numpy as np
p = np.zeros((101))
p[0]=1
p[1]=-3
p[100]=1
roots = np.roots(p)
for idx, root in enumerate(roots):
print(idx, root)
produces this output instantaneously:
0 (3.000000000000001+0j)
1 (-0.7364491456451218+0.6565561896636651j)
2 (-0.7364491456451218-0.6565561896636651j)
3 (-0.7764559201902995+0.6085861156452325j)
4 (-0.7764559201902995-0.6085861156452325j)
5 (-0.8133485650308432+0.5581912452828626j)
6 (-0.8133485650308432-0.5581912452828626j)
7 (-0.6934865839515425+0.701909773950447j)
8 (-0.6934865839515425-0.701909773950447j)
9 (-0.8469810844038753+0.5055727935082724j)
10 (-0.8469810844038753-0.5055727935082724j)
11 (-0.8772204006792861+0.4509407077743689j)
12 (-0.8772204006792861-0.4509407077743689j)
13 (-0.647738305184038+0.7444654479736014j)
14 (-0.647738305184038-0.7444654479736014j)
15 (-0.9039468754197537+0.39451284443370066j)
16 (-0.9039468754197537-0.39451284443370066j)
17 (-0.5993854422724829+0.7840527747018899j)
18 (-0.5993854422724829-0.7840527747018899j)
19 (-0.9270547780297581+0.3365141137728261j)
20 (-0.9270547780297581-0.3365141137728261j)
21 (-0.548619483695713+0.8205129677981756j)
22 (-0.548619483695713-0.8205129677981756j)
23 (-0.9464527000806124+0.2771755970853744j)
24 (-0.9464527000806124-0.2771755970853744j)
25 (-0.4956415264634955+0.8536995127614468j)
26 (-0.4956415264634955-0.8536995127614468j)
27 (-0.4406614924968664+0.8834787396172576j)
28 (-0.4406614924968664-0.8834787396172576j)
29 (-0.9620639136235793+0.21673363928004163j)
30 (-0.9620639136235793-0.21673363928004163j)
31 (-0.38389731168552527+0.909730344970996j)
32 (-0.38389731168552527-0.909730344970996j)
33 (-0.3255740750583158+0.9323478614682946j)
34 (-0.3255740750583158-0.9323478614682946j)
35 (0.7577303192949743+0.6394431221673114j)
36 (0.7577303192949743-0.6394431221673114j)
37 (0.7970347431023204+0.590099961131214j)
38 (0.7970347431023204-0.590099961131214j)
39 (0.7153872255455767+0.6861568685320916j)
40 (0.7153872255455767-0.6861568685320916j)
41 (0.8331341618753201+0.5383229631320452j)
42 (0.8331341618753201-0.5383229631320452j)
43 (0.6701830619131026+0.7300572029385581j)
44 (0.6701830619131026-0.7300572029385581j)
45 (0.8658742980131764+0.48431875063231544j)
46 (0.8658742980131764-0.48431875063231544j)
47 (0.6223059154766839+0.7709722084480215j)
48 (0.6223059154766839-0.7709722084480215j)
49 (0.5719535879849889+0.8087425205066434j)
50 (0.5719535879849889-0.8087425205066434j)
51 (0.8951137460294047+0.4283044061929457j)
52 (0.8951137460294047-0.4283044061929457j)
53 (0.5193328204049903+0.8432217744454027j)
54 (0.5193328204049903-0.8432217744454027j)
55 (0.9207248128533412+0.3705068199042141j)
56 (0.9207248128533412-0.3705068199042141j)
57 (0.46465850700695943+0.8742770284347632j)
58 (0.46465850700695943-0.8742770284347632j)
59 (0.9425943804458727+0.31116194515065604j)
60 (0.9425943804458727-0.31116194515065604j)
61 (-0.2659231616491491+0.9512390729535296j)
62 (-0.2659231616491491-0.9512390729535296j)
63 (0.4081528934442288+0.9017891596220862j)
64 (0.4081528934442288-0.9017891596220862j)
65 (0.9606247774115534+0.2505139365561644j)
66 (0.9606247774115534-0.2505139365561644j)
67 (0.9747346342048573+0.1888141457593689j)
68 (0.9747346342048573-0.1888141457593689j)
69 (0.35004475520869627+0.9256532298451866j)
70 (0.35004475520869627-0.9256532298451866j)
71 (-0.20518134277364738+0.966326373881672j)
72 (-0.20518134277364738-0.966326373881672j)
73 (0.2905685546336416+0.9457788166930109j)
74 (0.2905685546336416-0.9457788166930109j)
75 (0.9848596842823707+0.1263199581194814j)
76 (0.9848596842823707-0.1263199581194814j)
77 (-0.9738266720335937+0.15542892061869676j)
78 (-0.9738266720335937-0.15542892061869676j)
79 (0.2299635761582389+0.9620903055655939j)
80 (0.2299635761582389-0.9620903055655939j)
81 (-0.14358986755051278+0.977547071822796j)
82 (-0.14358986755051278-0.977547071822796j)
83 (0.1684730408262214+0.9745271385958778j)
84 (0.1684730408262214-0.9745271385958778j)
85 (0.9909534640600726+0.06329346693748208j)
86 (0.9909534640600726-0.06329346693748208j)
87 (0.9929878610066416+0j)
88 (-0.9816944521616785+0.09350551126383294j)
89 (-0.9816944521616785-0.09350551126383294j)
90 (0.10634320197349573+0.9830440167028471j)
91 (0.10634320197349573-0.9830440167028471j)
92 (-0.08139353360287407+0.9848536322040496j)
93 (-0.08139353360287407-0.9848536322040496j)
94 (0.043822424798379056+0.987611051554128j)
95 (0.043822424798379056-0.987611051554128j)
96 (-0.01883974695583218+0.9882138647642805j)
97 (-0.01883974695583218-0.9882138647642805j)
98 (-0.9856361368133812+0.031209912383584327j)
99 (-0.9856361368133812-0.031209912383584327j)
Is there some reason that this isn't good enough?
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
$endgroup$
add a comment |
-1
-1
-1
$begingroup$
I'm still not sure I understand the question, but this is easy with a computer, assuming you want numerical values. I wrote a python script to do this. (Annoyingly, numpy expects the leading coefficient $x^k$ of a polynomial of degre $n$ to be at index $n-k.$)
import numpy as np
p = np.zeros((101))
p[0]=1
p[1]=-3
p[100]=1
roots = np.roots(p)
for idx, root in enumerate(roots):
print(idx, root)
produces this output instantaneously:
0 (3.000000000000001+0j)
1 (-0.7364491456451218+0.6565561896636651j)
2 (-0.7364491456451218-0.6565561896636651j)
3 (-0.7764559201902995+0.6085861156452325j)
4 (-0.7764559201902995-0.6085861156452325j)
5 (-0.8133485650308432+0.5581912452828626j)
6 (-0.8133485650308432-0.5581912452828626j)
7 (-0.6934865839515425+0.701909773950447j)
8 (-0.6934865839515425-0.701909773950447j)
9 (-0.8469810844038753+0.5055727935082724j)
10 (-0.8469810844038753-0.5055727935082724j)
11 (-0.8772204006792861+0.4509407077743689j)
12 (-0.8772204006792861-0.4509407077743689j)
13 (-0.647738305184038+0.7444654479736014j)
14 (-0.647738305184038-0.7444654479736014j)
15 (-0.9039468754197537+0.39451284443370066j)
16 (-0.9039468754197537-0.39451284443370066j)
17 (-0.5993854422724829+0.7840527747018899j)
18 (-0.5993854422724829-0.7840527747018899j)
19 (-0.9270547780297581+0.3365141137728261j)
20 (-0.9270547780297581-0.3365141137728261j)
21 (-0.548619483695713+0.8205129677981756j)
22 (-0.548619483695713-0.8205129677981756j)
23 (-0.9464527000806124+0.2771755970853744j)
24 (-0.9464527000806124-0.2771755970853744j)
25 (-0.4956415264634955+0.8536995127614468j)
26 (-0.4956415264634955-0.8536995127614468j)
27 (-0.4406614924968664+0.8834787396172576j)
28 (-0.4406614924968664-0.8834787396172576j)
29 (-0.9620639136235793+0.21673363928004163j)
30 (-0.9620639136235793-0.21673363928004163j)
31 (-0.38389731168552527+0.909730344970996j)
32 (-0.38389731168552527-0.909730344970996j)
33 (-0.3255740750583158+0.9323478614682946j)
34 (-0.3255740750583158-0.9323478614682946j)
35 (0.7577303192949743+0.6394431221673114j)
36 (0.7577303192949743-0.6394431221673114j)
37 (0.7970347431023204+0.590099961131214j)
38 (0.7970347431023204-0.590099961131214j)
39 (0.7153872255455767+0.6861568685320916j)
40 (0.7153872255455767-0.6861568685320916j)
41 (0.8331341618753201+0.5383229631320452j)
42 (0.8331341618753201-0.5383229631320452j)
43 (0.6701830619131026+0.7300572029385581j)
44 (0.6701830619131026-0.7300572029385581j)
45 (0.8658742980131764+0.48431875063231544j)
46 (0.8658742980131764-0.48431875063231544j)
47 (0.6223059154766839+0.7709722084480215j)
48 (0.6223059154766839-0.7709722084480215j)
49 (0.5719535879849889+0.8087425205066434j)
50 (0.5719535879849889-0.8087425205066434j)
51 (0.8951137460294047+0.4283044061929457j)
52 (0.8951137460294047-0.4283044061929457j)
53 (0.5193328204049903+0.8432217744454027j)
54 (0.5193328204049903-0.8432217744454027j)
55 (0.9207248128533412+0.3705068199042141j)
56 (0.9207248128533412-0.3705068199042141j)
57 (0.46465850700695943+0.8742770284347632j)
58 (0.46465850700695943-0.8742770284347632j)
59 (0.9425943804458727+0.31116194515065604j)
60 (0.9425943804458727-0.31116194515065604j)
61 (-0.2659231616491491+0.9512390729535296j)
62 (-0.2659231616491491-0.9512390729535296j)
63 (0.4081528934442288+0.9017891596220862j)
64 (0.4081528934442288-0.9017891596220862j)
65 (0.9606247774115534+0.2505139365561644j)
66 (0.9606247774115534-0.2505139365561644j)
67 (0.9747346342048573+0.1888141457593689j)
68 (0.9747346342048573-0.1888141457593689j)
69 (0.35004475520869627+0.9256532298451866j)
70 (0.35004475520869627-0.9256532298451866j)
71 (-0.20518134277364738+0.966326373881672j)
72 (-0.20518134277364738-0.966326373881672j)
73 (0.2905685546336416+0.9457788166930109j)
74 (0.2905685546336416-0.9457788166930109j)
75 (0.9848596842823707+0.1263199581194814j)
76 (0.9848596842823707-0.1263199581194814j)
77 (-0.9738266720335937+0.15542892061869676j)
78 (-0.9738266720335937-0.15542892061869676j)
79 (0.2299635761582389+0.9620903055655939j)
80 (0.2299635761582389-0.9620903055655939j)
81 (-0.14358986755051278+0.977547071822796j)
82 (-0.14358986755051278-0.977547071822796j)
83 (0.1684730408262214+0.9745271385958778j)
84 (0.1684730408262214-0.9745271385958778j)
85 (0.9909534640600726+0.06329346693748208j)
86 (0.9909534640600726-0.06329346693748208j)
87 (0.9929878610066416+0j)
88 (-0.9816944521616785+0.09350551126383294j)
89 (-0.9816944521616785-0.09350551126383294j)
90 (0.10634320197349573+0.9830440167028471j)
91 (0.10634320197349573-0.9830440167028471j)
92 (-0.08139353360287407+0.9848536322040496j)
93 (-0.08139353360287407-0.9848536322040496j)
94 (0.043822424798379056+0.987611051554128j)
95 (0.043822424798379056-0.987611051554128j)
96 (-0.01883974695583218+0.9882138647642805j)
97 (-0.01883974695583218-0.9882138647642805j)
98 (-0.9856361368133812+0.031209912383584327j)
99 (-0.9856361368133812-0.031209912383584327j)
Is there some reason that this isn't good enough?
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
$endgroup$
I'm still not sure I understand the question, but this is easy with a computer, assuming you want numerical values. I wrote a python script to do this. (Annoyingly, numpy expects the leading coefficient $x^k$ of a polynomial of degre $n$ to be at index $n-k.$)
import numpy as np
p = np.zeros((101))
p[0]=1
p[1]=-3
p[100]=1
roots = np.roots(p)
for idx, root in enumerate(roots):
print(idx, root)
produces this output instantaneously:
0 (3.000000000000001+0j)
1 (-0.7364491456451218+0.6565561896636651j)
2 (-0.7364491456451218-0.6565561896636651j)
3 (-0.7764559201902995+0.6085861156452325j)
4 (-0.7764559201902995-0.6085861156452325j)
5 (-0.8133485650308432+0.5581912452828626j)
6 (-0.8133485650308432-0.5581912452828626j)
7 (-0.6934865839515425+0.701909773950447j)
8 (-0.6934865839515425-0.701909773950447j)
9 (-0.8469810844038753+0.5055727935082724j)
10 (-0.8469810844038753-0.5055727935082724j)
11 (-0.8772204006792861+0.4509407077743689j)
12 (-0.8772204006792861-0.4509407077743689j)
13 (-0.647738305184038+0.7444654479736014j)
14 (-0.647738305184038-0.7444654479736014j)
15 (-0.9039468754197537+0.39451284443370066j)
16 (-0.9039468754197537-0.39451284443370066j)
17 (-0.5993854422724829+0.7840527747018899j)
18 (-0.5993854422724829-0.7840527747018899j)
19 (-0.9270547780297581+0.3365141137728261j)
20 (-0.9270547780297581-0.3365141137728261j)
21 (-0.548619483695713+0.8205129677981756j)
22 (-0.548619483695713-0.8205129677981756j)
23 (-0.9464527000806124+0.2771755970853744j)
24 (-0.9464527000806124-0.2771755970853744j)
25 (-0.4956415264634955+0.8536995127614468j)
26 (-0.4956415264634955-0.8536995127614468j)
27 (-0.4406614924968664+0.8834787396172576j)
28 (-0.4406614924968664-0.8834787396172576j)
29 (-0.9620639136235793+0.21673363928004163j)
30 (-0.9620639136235793-0.21673363928004163j)
31 (-0.38389731168552527+0.909730344970996j)
32 (-0.38389731168552527-0.909730344970996j)
33 (-0.3255740750583158+0.9323478614682946j)
34 (-0.3255740750583158-0.9323478614682946j)
35 (0.7577303192949743+0.6394431221673114j)
36 (0.7577303192949743-0.6394431221673114j)
37 (0.7970347431023204+0.590099961131214j)
38 (0.7970347431023204-0.590099961131214j)
39 (0.7153872255455767+0.6861568685320916j)
40 (0.7153872255455767-0.6861568685320916j)
41 (0.8331341618753201+0.5383229631320452j)
42 (0.8331341618753201-0.5383229631320452j)
43 (0.6701830619131026+0.7300572029385581j)
44 (0.6701830619131026-0.7300572029385581j)
45 (0.8658742980131764+0.48431875063231544j)
46 (0.8658742980131764-0.48431875063231544j)
47 (0.6223059154766839+0.7709722084480215j)
48 (0.6223059154766839-0.7709722084480215j)
49 (0.5719535879849889+0.8087425205066434j)
50 (0.5719535879849889-0.8087425205066434j)
51 (0.8951137460294047+0.4283044061929457j)
52 (0.8951137460294047-0.4283044061929457j)
53 (0.5193328204049903+0.8432217744454027j)
54 (0.5193328204049903-0.8432217744454027j)
55 (0.9207248128533412+0.3705068199042141j)
56 (0.9207248128533412-0.3705068199042141j)
57 (0.46465850700695943+0.8742770284347632j)
58 (0.46465850700695943-0.8742770284347632j)
59 (0.9425943804458727+0.31116194515065604j)
60 (0.9425943804458727-0.31116194515065604j)
61 (-0.2659231616491491+0.9512390729535296j)
62 (-0.2659231616491491-0.9512390729535296j)
63 (0.4081528934442288+0.9017891596220862j)
64 (0.4081528934442288-0.9017891596220862j)
65 (0.9606247774115534+0.2505139365561644j)
66 (0.9606247774115534-0.2505139365561644j)
67 (0.9747346342048573+0.1888141457593689j)
68 (0.9747346342048573-0.1888141457593689j)
69 (0.35004475520869627+0.9256532298451866j)
70 (0.35004475520869627-0.9256532298451866j)
71 (-0.20518134277364738+0.966326373881672j)
72 (-0.20518134277364738-0.966326373881672j)
73 (0.2905685546336416+0.9457788166930109j)
74 (0.2905685546336416-0.9457788166930109j)
75 (0.9848596842823707+0.1263199581194814j)
76 (0.9848596842823707-0.1263199581194814j)
77 (-0.9738266720335937+0.15542892061869676j)
78 (-0.9738266720335937-0.15542892061869676j)
79 (0.2299635761582389+0.9620903055655939j)
80 (0.2299635761582389-0.9620903055655939j)
81 (-0.14358986755051278+0.977547071822796j)
82 (-0.14358986755051278-0.977547071822796j)
83 (0.1684730408262214+0.9745271385958778j)
84 (0.1684730408262214-0.9745271385958778j)
85 (0.9909534640600726+0.06329346693748208j)
86 (0.9909534640600726-0.06329346693748208j)
87 (0.9929878610066416+0j)
88 (-0.9816944521616785+0.09350551126383294j)
89 (-0.9816944521616785-0.09350551126383294j)
90 (0.10634320197349573+0.9830440167028471j)
91 (0.10634320197349573-0.9830440167028471j)
92 (-0.08139353360287407+0.9848536322040496j)
93 (-0.08139353360287407-0.9848536322040496j)
94 (0.043822424798379056+0.987611051554128j)
95 (0.043822424798379056-0.987611051554128j)
96 (-0.01883974695583218+0.9882138647642805j)
97 (-0.01883974695583218-0.9882138647642805j)
98 (-0.9856361368133812+0.031209912383584327j)
99 (-0.9856361368133812-0.031209912383584327j)
Is there some reason that this isn't good enough?
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
answered Mar 9 at 18:42
saulspatzsaulspatz
17.2k31435
17.2k31435
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1
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Welcome to MSE. Please give more context to this question, so people can give you appropriate answers. Is there a specific polynomial you are interested in? Are you looking for exact solutions or numerical ones? Are you only interested in real solutions, or do you want the complex ones, too? What have you tried?
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– saulspatz
Mar 9 at 17:57
$begingroup$
For example: x^100-3x^99+1=0. I need both real and complex solutions.
$endgroup$
– UNIBON
Mar 9 at 18:03
$begingroup$
Please add the context to the body of your question. Many people browsing questions will vote to close a question with no more context than this, without looking at the comments. Also, you ought to use MathJax to make your posts more readable. Look at how I edited the question.
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– saulspatz
Mar 9 at 18:11
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Thanks...I have tried downloading the mathjax but it wasn't successful.
$endgroup$
– UNIBON
Mar 9 at 18:22
1
$begingroup$
You don't need to download MathJax. You just put formatting commands in the text. For example
$x^{100}-3x^{99}+1=0$is displayed as $x^{100}-3x^{99}+1=0$$endgroup$
– saulspatz
Mar 9 at 18:24