Zeros of polynomials with random coefficients occur in many
scientific and engineering problems.
A general overview of the subject and references can be found in
the book of Bharucha-Reid and Sambandham [4], which is
the basic reference on this topic.
There is a wealth of information about distribution of zeros in the
complex plane and on the real line.
Almost all of the results are for coefficients chosen independently
from a common distribution that is continuous, and usually Gaussian.