Intersect a quartic to extract its roots

Raghavendra G. Kulkarni

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2017)

  • Volume: 16, Issue: 1, page 73-76
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Raghavendra G. Kulkarni. "Intersect a quartic to extract its roots." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16.1 (2017): 73-76. <http://eudml.org/doc/288295>.

@article{RaghavendraG2017,
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.},
author = {Raghavendra G. Kulkarni},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Intersection of curves; quartic polynomial; quadratic polynomial; roots; resolvent cubic equation},
language = {eng},
number = {1},
pages = {73-76},
title = {Intersect a quartic to extract its roots},
url = {http://eudml.org/doc/288295},
volume = {16},
year = {2017},
}

TY - JOUR
AU - Raghavendra G. Kulkarni
TI - Intersect a quartic to extract its roots
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2017
VL - 16
IS - 1
SP - 73
EP - 76
AB - 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.
LA - eng
KW - Intersection of curves; quartic polynomial; quadratic polynomial; roots; resolvent cubic equation
UR - http://eudml.org/doc/288295
ER -

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