  Stanley's non-negativity theorem is at the heart of many of the results in
Ehrhart theory. In this paper, we analyze the root behavior of general
polynomials satisfying the conditions of Stanley's theorem and compare this to
the known root behavior of Ehrhart polynomials. We provide a possible
counterexample to a conjecture of the second author, M. Beck, J. De Loera, J.
Pfeifle, and R. Stanley, and contribute some experimental data as well.
