Zeros and Critical Points of Polynomials Apolarity Apolar Locus Polar Derivative Polar Locus Complex Rolle's Theorem
Issue Date:
22-Nov-2010
Publisher:
University Press "Paisii Hilendarski", Plovdiv
Abstract:
Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients
and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of
the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n).
In this paper is found the smallest domain containing at leas one zero of the
derivative p0(z).
