Question 76
Let $f_1 \in \mathbb{R}[x]$ be a quadratic polynomial with positive leading coefficient. Set $f_{n+1} = f_1 \circ f_n$ for $n \ge 1$. It is known that the polynomial $f_2$ has four non-positive different zeroes. Prove that the polynomial $f_n$ has $2^n$ different real zeroes.