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ASU 149 All Soviet Union MO 1971 trinomials with real roots

Source:

July 3, 2019
algebrapolynomialtrinomial

Problem Statement

Prove that if the numbers p1,p2,q1,q2p_1, p_2, q_1, q_2 satisfy the condition (q1−q2)2+(p1−p2)(p1q2−p2q1)<0(q_1 - q_2)^2 + (p_1 - p_2)(p_1q_2 -p_2q_1)<0 then the square polynomials x2+p1x+q1x^2 + p_1x + q_1 and x2+p2x+q2x^2 + p_2x + q_2 have real roots, and between the roots of each there is a root of another one.
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