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Four distinct real solutions for a quadratic equation

Source: Morocco 2011

April 24, 2011
quadraticsalgebra unsolvedalgebra

Problem Statement

Prove that the equation x2+p∣x∣=qx−1x^{2}+p|x| = qx - 1 has 4 distinct real solutions if and only if p+∣q∣+2<0p+|q|+2<0 (pp and qq are two real parameters).
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