MathDB

4

Part of 2019 Latvia Baltic Way TST

Problems(1)

Polynomial problem with inequality

Source: Latvian TST for Baltic Way 2019 Problem 4

5/29/2020
Let P(x)P(x) be a polynomial with degree nn and real coefficients. For all 0≤y≤10 \le y \le 1 holds ∣p(y)∣≤1\mid p(y) \mid \le 1. Prove that p(−1n)≤2n+1−1p(-\frac{1}{n}) \le 2^{n+1} -1
algebrapolynomialinequalitieschebyshev polynomial