Cubic polynomial has root in segment [0,2]
Source: All-Russian Olympiad 2008 9.2,11.1
June 14, 2008
algebrapolynomialalgebra proposed
Problem Statement
Numbers are such that the equation x^3 \plus{} ax^2 \plus{} bx \plus{} c has three real roots.Prove that if \minus{} 2\leq a \plus{} b \plus{} c\leq 0,then at least one of these roots belongs to the segment