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no of roots of P(P(x)) = 0 vs P(x) = 0 - All-Russian MO 2002 Regional (R4) 11.5

Source:

September 17, 2024
algebrapolynomial

Problem Statement

Let P(x)P(x) be a polynomial of odd degree. Prove that the equation P(P(x))=0P(P(x)) = 0 has at least as many different real roots as the equation P(x)=0P(x) = 0
[hide=original wording]Пусть P(x) — многочлен нечетной степени. Докажите, что уравнение P(P(x)) = 0 имеет не меньше различных действительных корней, чем уравнение P(x) = 0