P(x) is a monic trinomial of degree 2 such that P(x) and P(P(P(x))) share a root. Prove that P(0)*P(1)=0.
P(x) = x^2 + bx + c
P(0)*P(1) = c(1+b+c) which is 0 if c = {0, (b+1)}
But since it is a trinomial then c cannot be zero.
So if it can be shown that P(x) and P(P(P(x))) share a root
iff (1+b+c) = 0, then that will constitute a proof.

Posted by Larry
on 20240621 13:03:08 