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(x - a) (x - c) + 2 (x - b) (x - d) = 0

Source: Polish MO second round 1953 p2

August 29, 2024
algebratrinomialpolynomial

Problem Statement

Prove that the equation (x−a)(x−c)+2(x−b)(x−d)=0, (x - a) (x - c) + 2 (x - b) (x - d) = 0, in which a<b<c<d a < b < c < d , has two real roots.
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