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Real roots of the equation P(P(x))=0

Source: Azerbaijan EGMO TST 2017, D2 P3

July 31, 2023
algebraPolynomialsReal Roots

Problem Statement

The degree of the polynomial P(x)P(x) is 2017.2017. Prove that the number of distinct real roots of the equation P(P(x))=0P(P(x)) = 0 is not less than the number of distinct real roots of the equation P(x)=0.P(x) = 0.
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