Roots of polynomial

General Mathematics
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Tolaso J Kos
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Roots of polynomial

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Post by Tolaso J Kos »

Let $p(x)$ be a non constant polynomial with real coefficients. If for every real $x$ the relation:

\begin{equation} p\left(x^2-1\right)=p(x)p(-x) \end{equation}

holds, find the maximum number of real roots of $p(x)$.
Hidden Message
The exercise is tremendously difficult. The answer to the problem is $4$ as the maximum number of real roots.
Imagination is much more important than knowledge.
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