MathDB
Polynomials - Iran NMO 2009 - Problem 1

Source:

September 20, 2010
algebrapolynomialquadraticsalgebra proposed

Problem Statement

Let p(x) p(x) be a quadratic polynomial for which : ∣p(x)∣≤1∀x∈{−1,0,1} |p(x)| \leq 1 \qquad \forall x \in \{-1,0,1\} Prove that:  ∣p(x)∣≤54∀x∈[−1,1] \ |p(x)|\leq\frac{5}{4} \qquad \forall x \in [-1,1]
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