Let G be a simple graph of order n and size m. An edge covering of the graph G is a set of edges such that every vertex of the graph is incident to at least one edge of the set. Let e(G,k) be the number of edge covering sets of G of size k. The edge cover polynomial of G is the polynomial In this paper, we obtain some results on the roots of the edge cover polynomials. We show that for every graph G with no isolated vertex, all the roots of E(G,x) are in the ball We prove that if every block of the graph G is K₂ or a cycle, then all real roots of E(G,x) are in the interval (−4,0]. We also show that for every tree T of order n we have where −ξ_R(T) is the smallest real root of E(T,x), and P_n,K_1,n−1 are the path and the star of order n, respectively.