Question 5
Let $f(x)$ be a nonconstant polynomial with real coefficients satisfying
$$f(x)f(2x^2)=f(2x^3+x)$$
for every $x\in\mathbb R$. Prove that $f$ has no real roots.
$$f(x)f(2x^2)=f(2x^3+x)$$
for every $x\in\mathbb R$. Prove that $f$ has no real roots.