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3 roots for f(f(x)) = 0, 7 f(f(x)) = 0 - All-Russian MO 2001 Regional (R4) 11.2

Source:

September 26, 2024
algebratrinomial

Problem Statement

The monic quadratic trinomial f(x)f(x) has 22 different roots. Could it be that the equation f(f(x))=0f(f(x)) = 0 has 33 different root, and the equation f(f(f(x)))=0f(f(f(x))) = 0 has 77 different roots?
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