The location of the zeros of the higher order derivatives of a polynomial

Let p(z) be a complex polynomial of degree n having k zeros in a disk D. We deal with the problem of finding the smallest concentric disk containing k - l zeros of p((l))(z). We obtain some estimates on the radius of this disk in general as well as in the special case, where k zeros in D are isolated from the other zeros of p(z). We indicate an application to the root-finding algorithms.