  This paper investigates the location of the zeros of a sequence of
polynomials generated by a rational function with a binomial-type denominator.
We show that every member of a two-parameter family consisting of such
generating functions gives rise to a sequence of polynomials
$\{P_{m}(z)\}_{m=0}^{\infty}$ that is eventually hyperbolic. Moreover, the real
zeros of the polynomials $P_{m}(z)$ form a dense subset of an interval
$I\subset\mathbb{R}^{+}$, whose length depends on the particular values of the
parameters in the generating function.
