Costa Rican Math Olympiad 2009 Problem 5
Source:
November 27, 2009
algebrapolynomialinequalitiesalgebra unsolved
Problem Statement
Suppose the polynomial x^{n} \plus{} a_{n \minus{} 1}x^{n \minus{} 1} \plus{} ... \plus{} a_{1} \plus{} a_{0} can be factorized as (x \plus{} r_{1})(x \plus{} r_{2})...(x \plus{} r_{n}), with real numbers.
Show that (n \minus{} 1)a_{n \minus{} 1}^{2}\geq\ 2na_{n \minus{} 2}