  Zeros of many ensembles of polynomials with random coefficients are
asymptotically equidistributed near the unit circumference. We give
quantitative estimates for such equidistribution in terms of the expected
discrepancy and expected number of roots in various sets. This is done for
polynomials with coefficients that may be dependent, and need not have
identical distributions. We also study random polynomials spanned by various
deterministic bases.
