MathDB
Four zeros of iterated quadratic trinomial

Source: All-Russian Olympiad 2006 finals, problem 10.7 = 9.8

May 7, 2006
quadraticsalgebra proposedalgebraquadratic equation

Problem Statement

Given a quadratic trinomial f(x)=x2+ax+bf\left(x\right)=x^2+ax+b. Assume that the equation f(f(x))=0f\left(f\left(x\right)\right)=0 has four different real solutions, and that the sum of two of these solutions is −1-1. Prove that b≤−14b\leq -\frac14.
Back to ProblemsView on AoPS