Let Q(x) be any polynomial of degree ≤n with real coefficients and let Mbe the maximum of Q(x)| on the interval [-1, 1]. Show then that|Q(x)| ≤ MTn (x)|for any |x|> 1.This is due to Chebyshev (1881).

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Answered: Let Q(x) be any polynomial of degree ≤…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 35E

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Let Q(x) be any polynomial of degree ≤ n with real coefficients and let M be the maximum of Q(x)| on the interval [-1, 1]. Show then that |Q(x)| ≤ M|T₁(x)| for any |x|> 1. This is due to Chebyshev (1881).