Simultaneous Approximation of all Real Zeroes of an Algebraic Polynomial

Abstract

The classical theorem of Descartes gives an upper bound for the number of the real positive zeroes of an algebraic polynomial with real coefficients by the number of the sign variations of its coefficients. A generalization of this theorem for the number of the complex zeroes of a polynomial with real coefficients in an angled domain was given by N. OBRESCHKOFF [1], and its extension for polynomials with complex coefficients was considered by I.J. SCHOENBERG [4].