MathDB
P(x)P''(x)≤P'(x)^2 if P has deg P roots

Source: Bulgaria 1991 P4

June 3, 2021
algebraPolynomials

Problem Statement

Let f(x)f(x) be a polynomial of degree nn with real coefficients, having nn (not necessarily distinct) real roots. Prove that for all real xx, f(x)f′′(x)≤f′(x)2.f(x)f''(x)\le f'(x)^2.
Back to ProblemsView on AoPS