On the zeros of a family of self-reciprocal polynomials

Abstract

The purpose of this paper is twofold. Firstly a sufficient condition is given to guarantee that all the zeros of self-reciprocal polynomials lie on the unit circle. Secondly it is shown that, for certain family of selfreciprocal polynomials with all its zeros on the unit circle, the convex combination also has all its zeros on the unit circle.