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ax^2 + 2bxy + cy^2 + 2dx + 2ey + f = P(x) Q(x)

Source: Polish MO Second Round 1962 p2

August 31, 2024
algebrapolynomial

Problem Statement

What conditions should real numbers a a , b b , c c , d d , e e , f f meet in order for a polynomial of second degree ax2+2bxy+cy2+2dx+2ey+fax^2 + 2bxy + cy^2 + 2dx + 2ey + f was the product of two first degree polynomials with real coefficients ?
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