1. Govil and Rahman [1, Theorem 1] have proved the fol- lowing theorem. n Theorem A. Let p (z) = £ aj^ k“0 z’^ ( 0) be a polynomiai of degree n with complex coefficients such that for some a >«-1 I a^ •11-2 a' I »ol- Then p (z) has ali its zeros in |z Kj, where Kj is the greatest positive root of the trinomial equation K"+ı - 2K" + 1 = 0. In the same paper [1], they also remark that Theorem A remains true if the polynomial has gaps and non-vanishing coef- ficients , an,’ satisfy a' a,‘n--ı“a I a°2 I O I a I a a”~' I aj We have sharpened the result for the polynomials having gaps and ■we prove Theorem 1. Let p (z) z= a„ z” + a„^ z“> a„ Z"2 +... ^2 / 0, be a polynomial of degree n with conıplex coefficients such that “2 1’ “2’- n,j ali being non-nega- tive integers. (ii) for some a >0, the coefficients a,j’s satisfy the condition ianl a“-“> a“-”*i2 |a„J.