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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 63, Pages 3389-3395

Zeros of an algebraic polynomial with nonequal means random coefficients

Department of Mathematics, University of Ulster, Jordanstown BT37 0QB, County Antrim, UK

Received 16 July 2004

Copyright © 2004 Hindawi Publishing Corporation. 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.


This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0+a1x+a2x2++an1xn1. The coefficients aj(j=0,1,2,,n1) are assumed to be independent normal random variables with nonidentical means. Previous results are mainly for identically distributed coefficients. Our result remains valid when the means of the coefficients are divided into many groups of equal sizes. We show that the behaviour of the random polynomial is dictated by the mean of the first group of the coefficients in the interval (1,1) and the mean of the last group in (,1)(1,).