This paper provides an asymptotic estimate for the expected number
of real zeros of a random algebraic polynomial a0+a1x+a2x2+⋯+an−1xn−1. The coefficients aj(j=0,1,2,…,n−1)
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,∞).