A remark on a note by Laguerre (Q1012383)

In 1880, Laguerre gave a way of getting an upper bound for the largest root of a polynomial having only real zeros. This relies on the assertion that for such a polynomial \(P\) of degree \(n\) one has \((n-1)P^{\prime 2}(x)- nP(x)P''(x)\geq 0\). The paper under review contains a generalization of this fact. Just as Laguerre did, the author applies the method to improve the bounds for the largest roots of orthogonal polynomials.