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Quadratic equations

Source: Finnish Mathematics Competition 2004, Final Round, Problem 1

November 14, 2011
quadraticsalgebra unsolvedalgebra

Problem Statement

The equations x2+2ax+b2=0x^2 +2ax+b^2 = 0 and x2+2bx+c2=0x^2 +2bx+c^2 = 0 both have two diff erent real roots. Determine the number of real roots of the equation x2+2cx+a2=0.x^2 + 2cx + a^2 = 0.
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