Hello,

given is a polynomial $\displaystyle P(x)=x^2+4x+2$. Find all solutions to the equation $\displaystyle P^n(x)=0$, where $\displaystyle P^n(x)=\underbrace{ P(P(...P }_{n}(x)...))$.

I have managed to work out that the solutions are of the form $\displaystyle \pm\sqrt[n+1]{2}-2$, but to prove it is quite a different matter. I tried induction but soon wound up in a pile of useless symbols. I depend on you with this one!