On the Sendov Conjecture for Polynomials with at Most Six Distinct Roots

In this paper we prove that Sendov’s conjecture is true for polynomials of degree ns6 we even determine the so-called extremal polynomials in this case., as well as for polynomials with at most six different zeros. We then generalize this last result to polynomials of degree n with at most n n. distinct roots, where n n. is an increasing and unbounded function of n.