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Malaysia IMONST 2 Senior Problem 5

Source: Malaysia IMO national selection test 2020

October 19, 2020
algebraquadratic equation

Problem Statement

Let pp and qq be real numbers such that the quadratic equation x2+px+q=0x^2 + px + q = 0 has two distinct real solutions x1x_1 and x2x_2. Suppose ∣x1−x2∣=1|x_1-x_2|=1, ∣p−q∣=1|p-q|=1. Prove that p,q,x1,x2p, q, x_1, x_2 are all integers.
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