Copyright © 2009 K. Farahmand and M. Sambandham. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The expected number of real zeros of an algebraic polynomial
with random coefficient is known. The distribution of the coefficients is often assumed to be identical albeit allowed to
have different classes of distributions. For the nonidentical case, there has been much interest where the variance of the th coefficient is . It is shown that this class of polynomials has significantly more zeros than the classical
algebraic polynomials with identical coefficients. However, in the case of nonidentically distributed coefficients it is
analytically necessary to assume that the means of coefficients are zero. In this work we study a case when the moments of the coefficients have both binomial and geometric progression elements. That is we assume and . We show how the above expected number of real zeros is dependent on values of and in various cases.