MathDB
Regional Olympiad - FBH 2016 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

September 22, 2018
algebrainequalities

Problem Statement

If ∣ax2+bx+c∣≤1\mid ax^2+bx+c \mid \leq 1 for all x∈[−1,1]x \in [-1,1] prove that: a)a) ∣c∣≤1\mid c \mid \leq 1 b)b) ∣a+c∣≤1\mid a+c \mid \leq 1 c)c) a2+b2+c2≤5a^2+b^2+c^2 \leq 5
Back to ProblemsView on AoPS