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NZ-NZMO 2020 Problem 1

  • Answer

Let P(x)=x3−2x+1P(x) = x^{3} - 2x + 1 and let Q(x)=x3−4x2+4x−1Q(x) = x^{3} - 4x^{2} + 4x - 1 . Show that

if P(r)=0P(r) = 0 then Q(r2)=0Q(r^{2}) = 0

Dataset text NuminaMath olympiads. Quoted with source.

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