Zero-Free Region for Polynomials with Restricted Coefficients

In this paper we prove some extension of the Enestrm-Kakeya theorem says that. Let P (z) = -_ (i=0) ^n-a_i z^i be a polynomial of degree n such that 0less thana_ (0) -a_1- a_2-, -, -a_n then all the zeros of P (z) lie in |z|-1. By relaxing the hypothesis of this result in several ways and obtain zero-free regions for polynomials with restricted coefficients and there by present some interesting generalizations and extensions of the Enestrom-Kakeya Theorem