The expected number of real zeros of an algebraic polynomial a_0+1x+2x~2+···+a_nx~nwith randomcoefficient ai, j = 0, 1, 2, ... , n is known. The distribution of the coefficients is often assumed to beidentical albeit allowed to have different classes of distributions. For the nonidentical case, therehas been much interest where the variance of the jth coefficient is var (a1) = ( ). It is shownthat this class of polynomials has significantly more zeros than the classical algebraic polynomialswith identical coefficients. However, in the case of nonidentically distributed coefficients it isanalytically necessary to assume that the means of coefficients are zero. In this work we study acase when the moments of the coefficients have both binomial and geometric progression elements.That is we assume E(aj) = (7)1,1+1 and var (a1) = (7)o-21. We show how the above expectednumber of real zeros is dependent on values of a2 and 14 in various cases.
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