MathDB
integer f(x) = x ^ 2 + ax + b, with f (x) >= - 9/ 10, Prove f (x)>= - 1/4

Source: Tuymaada Junior 2005 p5

May 12, 2019
quadratic trinomialtrinomialalgebra

Problem Statement

Given the quadratic trinomial f(x)=x2+ax+b f (x) = x ^ 2 + ax + b with integer coefficients, satisfying the inequality f(x)≥−910 f (x) \geq - {9 \over 10} for any x x . Prove that f(x)≥−14 f (x) \geq - {1 \over 4} for any x x .
Back to ProblemsView on AoPS