  From a sequence $\left\{ a_{n}\right\} _{n=0}^{\infty}$ of real numbers
satisfying a three-term recurrence, we form a sequence of polynomials $\left\{
P_{m}(z)\right\} _{m=0}^{\infty}$ whose coefficients are numbers in this
sequence. We showed that under explicit conditions, the zeros of $P_{m}(z)$,
$m\gg1$, lie on one side of the circle whose radius is given by modulus of a
zero of the denominator of the generating function of $\left\{ a_{n}\right\}
_{n=0}^{\infty}$.
