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Nice quadratic problem

Source: ARO 2021 9.5

April 20, 2021
algebra

Problem Statement

The reals b>0b>0 and aa are such that the quadratic x2+ax+bx^2+ax+b has two distinct real roots, exactly one of which lies in the interval [−1;1][-1;1]. Prove that one of the roots lies in the interval (−b;b)(-b;b).
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