Let $\displaystyle $$a \in {{\Cal R}^*}$$$ and $\displaystyle $$b,c \in {\Cal R}$$$ such that $\displaystyle $$4ac < {\left( {b - 1} \right)^2}$$$. Let $\displaystyle $$f:{\Cal R} \to {\Cal R}$$$ be a function such that $\displaystyle $$f\left( {a{x^2} + bx + c} \right) = a{f^2}\left( x \right) + bf\left( x \right) + c,\forall x \in {\Cal R}$$$. Prove that $\displaystyle $$f\left( {f\left( x \right)} \right) = x$$$ has at least one root