Remark on "When Are All the Zeros of a Polynomial Real and Distinct?"

The purpose of this note is to point out that the main result of [M. Chamberland, When Are All the Zeros of a Polynomial Real and Distinct? Amer. Math. Monthly. 127 (2020) 449-451] is implicitly contained in the elementary lore of the theory of orthogonal polynomials on the real line.