<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.</p></abstract>

In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.

Intersect a quartic to extract its roots

Department of Electronics & Communication Engineering

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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{"article-title":"Intersect a quartic to extract its roots"}

In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the...

Intersect a quartic to extract its roots

Published Online: Jan 27, 2018

Page range: 73 - 76

Received: Sep 25, 2017

Accepted: Nov 04, 2017

DOI: https://doi.org/10.1515/aupcsm-2017-0006

Keywords
Intersection of curves, quartic polynomial, quadratic polynomial, roots, resolvent cubic equation

© 2017 Raghavendra G. Kulkarni, published by De Gruyter Open

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Intersect a quartic to extract its roots

Published Online: Jan 27, 2018

Page range: 73 - 76

Received: Sep 25, 2017

Accepted: Nov 04, 2017

DOI: https://doi.org/10.1515/aupcsm-2017-0006

KeywordsIntersection of curves, quartic polynomial, quadratic polynomial, roots, resolvent cubic equation

© 2017 Raghavendra G. Kulkarni, published by De Gruyter Open

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Keywords
Intersection of curves, quartic polynomial, quadratic polynomial, roots, resolvent cubic equation