A REMARK ON SENDOV CONJECTURE

Sendov conjecture asserts that, for a polynomial with each zero located inside the closed unit disk in the complex plane, it must be the case that every closed disk of radius 1 centred at a zero will contain a critical point of it. The conjecture has been proved for polynomials of degree less than or equal to 8. In this article we present the shortest approach of solving this problem using famous Theorem of Grace on apolar polynomials. The case for polynomials of degree at most three is illustrated over here and the author believes that the technique can be extended to higher degree polynomials also.