Let $P(\epsilon)$ is polynomial of order $N$ and $Q(\epsilon)$ is a polynomial of order $n$, where $N=n\times$integer. Is there any relation with the solutions of $Q(\epsilon)$ and $P(\epsilon)$? Is there any proof for that? Thanks
Comparing solutions of higher order polynomial with a lower order polynomial
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polynomials
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1No, a relation between degrees does not constrain the coefficients of $P$ and $Q$, so there is expected to be no relation between the roots of $P$ and $Q$. – 2017-01-10
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0You are welcome. Since your question has been answered, I request you to close this question, by accepting the below answer. You can choose to wait, but by the looks of it, you are satisfied. – 2017-01-10
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For "proof" that there is no relation, take $P = x^4$ and $Q = x^2 - 4$ as a counterexample.