In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form
$$f_{n}(z)=\sum\limits_{j=0}^{n}{a^{n}_{j}}{c^{n}_{j}}z^{j}$$
where
\({a^{n}_{j}}\) are independent and identically distributed real random variables with bounded (2 +
δ)th absolute moment and the deterministic numbers
\({c^{n}_{j}}\) are normalizing constants for the monomials
z j within a weighted
L 2-space induced by a radial weight function satisfying suitable smoothness and growth conditions.