Zeros of a binomial combination of Chebyshev polynomials

For 0 < alpha < 1, we study the zeros of the sequence of polynomials {P-m(z)}(m=0)(infinity) generated by the reciprocal of (1 - t)(alpha)(1 - 2zt + t(2)), expanded as a power series in t. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of P-m(z) outside the interval (-1, 1) is bounded by a constant independent of m.