A systematic approach to the exact roots of polynomials

Serdar Beji

doi:10.1007/s00009-008-0141-6

A systematic approach to the exact roots of polynomials

Serdar Beji^*

^*Corresponding author for this work

Department of Shipbuilding and Ocean Engineering

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	163-172
Number of pages	10
Journal	Mediterranean Journal of Mathematics
Volume	5
Issue number	2
DOIs	https://doi.org/10.1007/s00009-008-0141-6
Publication status	Published - Jun 2008

Keywords

Cardan and Cardan-Ferrari Solutions
Systematic approach
Zeros of the second, third, and fourth degree polynomials

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10.1007/s00009-008-0141-6

Cite this

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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.",

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AB - 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.

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KW - Zeros of the second, third, and fourth degree polynomials

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A systematic approach to the exact roots of polynomials

Abstract

Keywords

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