Continuity of the roots of a polynomial

Abstract

Let K be an algebraically closed field with an absolute value. This note gives a simple proof of the classical result that the roots of a polynomial with coefficients in K are continuous functions of the coefficients of the polynomial.

KEYWORDS:

• Continuity of roots
• deformations of polynomial
• elementary methods
• polynomials
• roots of polynomials

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 12D10
• 12E05
• 12J10
• 12L15