Question 53
Let $P(x)$ be a non-constant polynomial with real coefficients such that all of its roots are real numbers. Suppose that there exists a polynomial $Q(x)$ with real coefficients such that
$$
(P(x))^2 = P(Q(x))
$$
for all real numbers $x$. Prove that all roots of $P(x)$ are equal.
$$
(P(x))^2 = P(Q(x))
$$
for all real numbers $x$. Prove that all roots of $P(x)$ are equal.