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RU-ALLRUSSIAN 1973 Problem 7

    Define p(x)=ax2+bx+c\mathrm{p(x) = ax^2 + bx + c} . If p(x)=x\mathrm{p(x) = x} has no real roots, prove that p(p(x))=0\mathrm{p(p(x)) = 0} has no real roots.

    Dataset text NuminaMath olympiads. Quoted with source.

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