BY-MO 1995 Problem 6

Let $p$ and $q$ be distinct positive integers. Prove that at least one of the equations $x^2+px+q=0$ and $x^2+qx+p=0$ has a real root.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.