Abstract

The famous Enestr\"{o}m-Kakeya Theorem states that a polynomial $ P(z)=\sum_{i=0}^{n} a_iz^i$ with real positive coefficients satisfying $0\textless {a_0}\leq {a_1}\leq...\leq{a_n}$ has all its zeros in $|z|\leq{1}$. Various generalizations of this result are available in the literature. In this paper we put certain restrictions on the real and imaginary parts of the coefficients of a polynomial and find annular regions containing all the zeros of the polynomial. Our results generalize many results already known in the literature. 

Keywords and Phrases

Zeros of polynomial, Enestr\"{o}m-Kakeya theorem.

A.M.S. subject classification

12D10, 26C10 30C10, 30C15.

.....