Polynomials satisfying condition $P(x^2)=P(-x)P(x)$. [closed]
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I need some help in finding out the number of polynomials P having degree 4 with real coefficients such that $P(x^2)=P(-x)P(x)$. Please don't use the brute force method of checking every condition established by the general equation.
algebra-precalculus polynomials
edited Nov 25 at 16:30
Yadati Kiran
1,289417
asked Nov 25 at 16:21
RudrakshJ
122
closed as off-topic by GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3 Nov 25 at 16:42
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3
If this question can be reworded to fit the rules in the help center, please edit the question.
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I need some help in finding out the number of polynomials P having degree 4 with real coefficients such that $P(x^2)=P(-x)P(x)$. Please don't use the brute force method of checking every condition established by the general equation.
algebra-precalculus polynomials
edited Nov 25 at 16:30
Yadati Kiran
1,289417
asked Nov 25 at 16:21
RudrakshJ
122
closed as off-topic by GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3 Nov 25 at 16:42
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3
If this question can be reworded to fit the rules in the help center, please edit the question.
4
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 25 at 16:22
1
@RudrakshJ: Please share with us what you have done.
– Yadati Kiran
Nov 25 at 16:23
@hamam_Abdallah $1-x$ is not of degree $4$
– saulspatz
Nov 25 at 16:30
$x^4$ is a solution.
– hamam_Abdallah
Nov 25 at 16:32
BTW, to edit your question, you can click the word "edit" below the question itself.
– John Hughes
Nov 25 at 16:37
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show 1 more comment
up vote
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down vote
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up vote
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down vote
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I need some help in finding out the number of polynomials P having degree 4 with real coefficients such that $P(x^2)=P(-x)P(x)$. Please don't use the brute force method of checking every condition established by the general equation.
algebra-precalculus polynomials
edited Nov 25 at 16:30
Yadati Kiran
1,289417
asked Nov 25 at 16:21
RudrakshJ
122
I need some help in finding out the number of polynomials P having degree 4 with real coefficients such that $P(x^2)=P(-x)P(x)$. Please don't use the brute force method of checking every condition established by the general equation.
algebra-precalculus polynomials
algebra-precalculus polynomials
edited Nov 25 at 16:30
Yadati Kiran
1,289417
asked Nov 25 at 16:21
RudrakshJ
122
edited Nov 25 at 16:30
Yadati Kiran
1,289417
asked Nov 25 at 16:21
RudrakshJ
122
edited Nov 25 at 16:30
Yadati Kiran
1,289417
edited Nov 25 at 16:30
Yadati Kiran
1,289417
edited Nov 25 at 16:30
Yadati Kiran
1,289417
1,289417
asked Nov 25 at 16:21
RudrakshJ
122
asked Nov 25 at 16:21
RudrakshJ
122
asked Nov 25 at 16:21
RudrakshJ
122
122
closed as off-topic by GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3 Nov 25 at 16:42
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3 Nov 25 at 16:42
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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, Ennar, greedoid, John Hughes, kingW3
If this question can be reworded to fit the rules in the help center, please edit the question.
4
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 25 at 16:22
1
@RudrakshJ: Please share with us what you have done.
– Yadati Kiran
Nov 25 at 16:23
@hamam_Abdallah $1-x$ is not of degree $4$
– saulspatz
Nov 25 at 16:30
$x^4$ is a solution.
– hamam_Abdallah
Nov 25 at 16:32
BTW, to edit your question, you can click the word "edit" below the question itself.
– John Hughes
Nov 25 at 16:37
|
show 1 more comment
4
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 25 at 16:22
1
@RudrakshJ: Please share with us what you have done.
– Yadati Kiran
Nov 25 at 16:23
@hamam_Abdallah $1-x$ is not of degree $4$
– saulspatz
Nov 25 at 16:30
$x^4$ is a solution.
– hamam_Abdallah
Nov 25 at 16:32
BTW, to edit your question, you can click the word "edit" below the question itself.
– John Hughes
Nov 25 at 16:37
4
4
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 25 at 16:22
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 25 at 16:22
1
1
@RudrakshJ: Please share with us what you have done.
– Yadati Kiran
Nov 25 at 16:23
@RudrakshJ: Please share with us what you have done.
– Yadati Kiran
Nov 25 at 16:23
@hamam_Abdallah $1-x$ is not of degree $4$
– saulspatz
Nov 25 at 16:30
@hamam_Abdallah $1-x$ is not of degree $4$
– saulspatz
Nov 25 at 16:30
$x^4$ is a solution.
– hamam_Abdallah
Nov 25 at 16:32
$x^4$ is a solution.
– hamam_Abdallah
Nov 25 at 16:32
BTW, to edit your question, you can click the word "edit" below the question itself.
– John Hughes
Nov 25 at 16:37
BTW, to edit your question, you can click the word "edit" below the question itself.
– John Hughes
Nov 25 at 16:37
|
show 1 more comment
1 Answer
1
active
oldest
votes
up vote
0
down vote
hint
Assume $P(0)=0$
then
$$P(x)=xQ(x)$$
with
$$Q(x^2)=-Q(x)Q(-x)$$
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
hint
Assume $P(0)=0$
then
$$P(x)=xQ(x)$$
with
$$Q(x^2)=-Q(x)Q(-x)$$
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
add a comment |
up vote
0
down vote
hint
Assume $P(0)=0$
then
$$P(x)=xQ(x)$$
with
$$Q(x^2)=-Q(x)Q(-x)$$
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
add a comment |
up vote
0
down vote
up vote
0
down vote
hint
Assume $P(0)=0$
then
$$P(x)=xQ(x)$$
with
$$Q(x^2)=-Q(x)Q(-x)$$
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
hint
Assume $P(0)=0$
then
$$P(x)=xQ(x)$$
with
$$Q(x^2)=-Q(x)Q(-x)$$
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
answered Nov 25 at 16:31
hamam_Abdallah
37.5k21634
37.5k21634
add a comment |
add a comment |
4
Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
– José Carlos Santos
Nov 25 at 16:22
1
@RudrakshJ: Please share with us what you have done.
– Yadati Kiran
Nov 25 at 16:23
@hamam_Abdallah $1-x$ is not of degree $4$
– saulspatz
Nov 25 at 16:30
$x^4$ is a solution.
– hamam_Abdallah
Nov 25 at 16:32
BTW, to edit your question, you can click the word "edit" below the question itself.
– John Hughes
Nov 25 at 16:37