## Roots of $f(f(..f(x)..))$, where $ f(x) = ax^2 + bx + c $, are symmetric about $ \frac{-b}{2a} $

Posted on Thu 30 April 2020 in Mathematics

Define $ f(x) = ax^2 + bx + c , a,b,c \in \mathbb{R}$ and $ f^n(x) = f(f^{n-1}(x)), n>1 $. Prove that the real roots of $ f^n(x) $ are symmetric about the vertical line passing through vertex i.e. $ x = \frac{-b}{2a} $

This seems like …

Continue reading