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ASU 180 All Soviet Union MO 1973 ax^2+bx+c=x has not real roots

Source:

July 4, 2019
trinomialalgebra

Problem Statement

The square polynomial f(x)=ax2+bx+cf(x)=ax^2+bx+c is of such a sort, that the equation f(x)=xf(x)=x does not have real roots. Prove that the equation f(f(x))=0f(f(x))=0 does not have real roots also.
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