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Parametrized inequality

Source: Czech and Slovak Olympiad 1981, National Round, Problem 1

October 11, 2024
inequalitiesalgebraparameterization

Problem Statement

Determine all a∈Ra\in\mathbb R such that the inequality x4+x3−2(a+1)x2−ax+a2<0x^4+x^3-2(a+1)x^2-ax+a^2<0 has at least one real solution x.x.
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