On the Number of Real Zeros of a Certain Kind of Polynomials

Abstract

In the present paper we consider the polynomials of the type q_n (x) = (x+1)ⁿ P (x)+xⁿ Q (x), where P (x) and Q(x) are nonconstant polynomials with real coefficients of degree m such that \(\lim\limits_{x\to\pm\infty}\frac{P(x)}{Q(x)}\) is a finite positive number. We investigate the number of real zeros of q_n(x) when \(n\to\infty\).