Let G be a finite group.For k ∈ N,x ∈ Irr(G),define cx(k):=1/|G| Σg∈G x(gk).This is called the k-th Frobenius-Schur indicator of x.In this article we study the Frobenius-Schur indicators for Frobenius groups,p-groups,semidihedral groups and modular p-groups.Further,we use this to study the function ζG(g) which counts the number of roots of xk =g in a finite group G.