A systematic approach to the exact roots of polynomials

Beji S.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.5, no.2, pp.163-172, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1007/s00009-008-0141-6
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.163-172
  • Istanbul Technical University Affiliated: No

Abstract

A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel's proof, the method produces no solution for the quintic equation.