Yet another proof that the roots of a polynomial depend continuously on the coefficients

Publication date: 30 June 2022

Abstract: The roots of a complex polynomial depend continuously on the coefficients; that is, an infinitesimal perturbation of the coefficients results in an infinitesimal perturbation of the roots. A short, straightforward proof of this is possible using infinitesimals.

Mathematics Subject Classification ID

Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Nonstandard models in mathematics (03H05) Nonstandard arithmetic and field theory (12L15)

This page was built for publication: Yet another proof that the roots of a polynomial depend continuously on the coefficients

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6403695)