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Real roots of quadratics imply real roots of other quadratic

Source: XVIII Olimpíada Matemática Rioplatense (2009)

July 23, 2011
quadraticsalgebra unsolvedalgebra

Problem Statement

Find all pairs (a,b)(a, b) of real numbers with the following property: Given any real numbers cc and dd, if both of the equations x2+ax+1=cx^2+ax+1=c and x2+bx+1=dx^2+bx+1=d have real roots, then the equation x2+(a+b)x+1=cdx^2+(a+b)x+1=cd has real roots.
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