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f(x) = x^2 + ax + b cos x - All-Russian MO 1998 Regional (R4) 10.1

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September 17, 2024
algebratrigonometry

Problem Statement

Let f(x)=x2+ax+bcosxf(x) = x^2 + ax + b cos x. Find all values of parametera a and bb, for which the equations f(x)=0f(x) = 0 and f(f(x))=0f(f(x)) = 0 have the same non-empty sets of real roots.
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