On the Number of Real Solutions of a Random Polynomial

We obtain bounds as a function of n, for the number of real solutions of the random algebraic equation njs0 aj x jsKn where the coefficients aj’s are independent random variables and Kn is a sequence of real numbers with suitably specified growth. Both cases of finite and infinite variances are considered. When all Kn are set to a constant K it is shown how these bounds on the number of real solutions are a decreasing function of K.