Consider a polynomial of the following type:(adsbygoogle = window.adsbygoogle || []).push({});

A_n w^n + A_{n-1} w^{n-1}k + A_{n-2} w^{n-2} k^2 + ... + A_1 k^n =0

What are the general conditions on {A_i} in order for the roots w(k) to be EITHER real OR functions with even imaginary parts, Im[w[k]]=Im[w[-k]]?

I would be interested in whether anyone has ever worked on this problem, or if this problem was ever shown to be unsolvable (perhaps there is a trivial connection to, e.g., Galois theory I missed).

Thanks, and best

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# A general condition on polynomial roots

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