Some results for the Sendov conjecture

The Sendov conjecture may be stated as: If all zeros of a complex polynomial p(z) lie in \z\ less than or equal to 1, then there is always a zero of p'(z) in \z - a\ less than or equal to 1, where a is any zero of p(z). We find several easy to apply conditions for which this conjecture is true for polynomials of degree n. Ranges of values of a implied by these conditions are also given. (C) 1996 Academic Press, Inc.