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Determine whether there exist two real numbers a and b

Source: Canadian Repêchage 2012: Problem 6

May 19, 2014
calculusderivativequadraticsalgebra solvedalgebra

Problem Statement

Determine whether there exist two real numbers aa and bb such that both (x−a)3+(x−b)2+x(x-a)^3+ (x-b)^2+x and (x−b)3+(x−a)2+x(x-b)^3 + (x-a)^2 +x contain only real roots.
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