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Quadratics with Common Roots

Source: All-Russian MO 2000

December 30, 2012
quadraticsalgebra unsolvedalgebra

Problem Statement

Let a,b,ca,b,c be distinct numbers such that the equations x2+ax+1=0x^2+ax+1=0 and x2+bx+c=0x^2+bx+c=0 have a common real root, and the equations x2+x+a=0x^2+x+a=0 and x2+cx+bx^2+cx+b also have a common real root. Compute the sum a+b+ca+b+c.
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