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polynomial with real coefficients

Source: IMC 1998 day 1 problem 5

November 1, 2005
algebrapolynomialinductionreal analysisreal analysis unsolved

Problem Statement

Let PP be a polynomial of degree nn with only real zeros and real coefficients. Prove that for every real xx we have (n−1)(P′(x))2≥nP(x)P′′(x)(n-1)(P'(x))^2\ge nP(x)P''(x). When does equality occur?
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