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Chisinau MO p17 1949-56 VIII-IX x^2+px+q+(x+a)(2x+p)=0 has real roots for any a

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March 15, 2021
algebratrinomialparameter

Problem Statement

Prove that if the roots of the equation x2+px+q=0x^2 + px + q = 0 are real, then for any real number aa the roots of the equation x2+px+q+(x+a)(2x+p)=0x^2 + px + q + (x + a) (2x + p) = 0 are also real.
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