  Our goal in this paper is to study the zero distribution of a sequence of
polynomials whose coefficients satisfy a three-term recurrence. Equivalently,
these polynomials are Taylor polynomials of a rational function with a
polynomial denominator of degree 2. We will use complex analysis to find the
bi-variate generating function for that sequence of Taylor polynomials. With
this generating function, we prove that the zeros of these Taylor polynomials
lie on one side of the closed disk centered at the origin. The radius of the
disk is exactly the reciprocal of the modulus of the smaller zero of the degree
two denominator. Finally, we show that the zeros of these Taylor polynomials
approach the boundary of the disk above.
