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(n - q)^2 - (m - p) (np - mq) = 0

Source: Polish MO second round 1951 p4

August 28, 2024
algebratrinomial

Problem Statement

Prove that if equations x2+mx+n=0    and    x2+px+q=0x^2 + mx + n = 0 \,\,\,\, and\,\, \,\, x^2 + px + q = 0 have a common root, there is a relationship between the coefficients of these equations
(n−q)2−(m−p)(np−mq)=0. (n - q)^2 - (m - p) (np - mq) = 0.
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