Zeros of orthogonal polynomials on the real line

Let $p_n(x)$ be orthogonal polynomials associated to a measure $d\mu$ of compact support in $R$. If $E\in ̸supp(d\mu )$, we show there is a $\delta >0$ so that for all $n$, either $p_n$ or $p_{n+1}$ has no zeros in $(E-\delta, E+\delta)$\mathrm{.}If$E$isanisolatedpointof$supp(d\mu)$,weshowthereisa$\delta$sothatforall$n$,either$p_n$or$p_{n+1}$hasatmostonezeroin$(E-\delta, E+\delta)$\mathrm{.}Weprovideanexamplewherethezerosof$p_n$ are dense in a gap of $supp(d\mu )$.