MathDB
Polynomial with real roots

Source: Turkey TST 2019 Day 2 P5

March 26, 2019
algebrapolynomial

Problem Statement

P(x)P(x) is a nonconstant polynomial with real coefficients and its all roots are real numbers. If there exist a Q(x)Q(x) polynomial with real coefficients that holds the equality for all xx real numbers (P(x))2=P(Q(x))(P(x))^{2}=P(Q(x)), then prove that all the roots of P(x)P(x) are same.
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