A class of orthogonal polynomials

The order of the distance between zeros of orthogonal and of quasiorthogonal polynomials is determined, and also the order of the Christoffel function if the weight function $w(x)=q(x)e^{-x}$ satisfies certain conditions. As a special case, lower and upper bounds are found for the distance between zeros of $L_n^\alpha(x)+AL_{n-1}^\alpha(x)$, where $L_n^\alpha$ is the $n$-th order Laguerre polynomial.