A Classic New Method to Solve Quartic Equations

Amir Fathi; Nastaran Sharifan

doi:doi:10.11648/j.acm.20130202.11

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A Classic New Method to Solve Quartic Equations

Amir Fathi, Nastaran Sharifan

Published in Applied and Computational Mathematics (Volume 2, Issue 2)

Published: 2 April 2013

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Abstract

Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.

Published in	Applied and Computational Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.acm.20130202.11
Page(s)	24-27
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Fourth Degree Polynomial, Quartic Equation

References

[1]	"A Simple Method to Solve Quartic Equations" Amir Fathi, Pooya Mobadersany, Rahim Fathi, Australian Journal of Basic and Applied Sciences, 6(6): 331-336, 2012, ISSN 1991-8178.
[2]	Cardano, Girolamo, (translated by T. Richard Witmer), Ars Magna or the Rules of Algebra, Dover, New York, NY, 1993.
[3]	Faucette, W. M. "A Geometric Interpretation of the Solution of the General Quartic Polynomial." Amer. Math. Monthly 103, 51-57, 1996.
[4]	Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989.
[5]	Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, 1988.
[6]	MathPages. "Reducing Quartics to Cubics." http://www.mathpages.com/home/kmath296.htm.
[7]	Smith, D. E. A Source Book in Mathematics. New York: Dover, 1994.
[8]	van der Waerden, B. L. §64 in Algebra, Vol. 1. New York: Springer-Verlag, 1993.
[9]	Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 12, 1987a.
[10]	Beyer, W. H. Handbook of Mathematical Sciences, 6th ed. Boca Raton, FL: CRC Press, 1987b.
[11]	Birkhoff, G. and Mac Lane, S. A Survey of Modern Algebra, 5th ed. New York: Macmillan, pp. 107-108, 1996.
[12]	Borwein, P. and Erdélyi, T. "Quartic Equations." §1.1.E.1e in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, p. 4, 1995.
[13]	Boyer, C. B. and Merzbach, U. C. A History of Mathematics, 2nd ed. New York: Wiley, pp. 286-287, 1991.
[14]	I. Stewart, "Galois theory," ed: Chapman & Hall/CRC Mathematics, 2004.
[15]	J. J. O'Connor and E. F. Robertson, "Lodovico Ferrari," in The MacTutor History of Mathematics archive, ed. School of Mathematics and Statistics, University of St Andrews Scotland.
[16]	AN EASY LOOK AT THE CUBIC FORMULA .Thomas J. Osler.Mathematics Department, Rowan University, Glassboro NJ 08028.

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APA Style

Amir Fathi, Nastaran Sharifan. (2013). A Classic New Method to Solve Quartic Equations. Applied and Computational Mathematics, 2(2), 24-27. https://doi.org/10.11648/j.acm.20130202.11

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ACS Style

Amir Fathi; Nastaran Sharifan. A Classic New Method to Solve Quartic Equations. Appl. Comput. Math. 2013, 2(2), 24-27. doi: 10.11648/j.acm.20130202.11

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AMA Style

Amir Fathi, Nastaran Sharifan. A Classic New Method to Solve Quartic Equations. Appl Comput Math. 2013;2(2):24-27. doi: 10.11648/j.acm.20130202.11

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@article{10.11648/j.acm.20130202.11,
  author = {Amir Fathi and Nastaran Sharifan},
  title = {A Classic New Method to Solve Quartic Equations},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {24-27},
  doi = {10.11648/j.acm.20130202.11},
  url = {https://doi.org/10.11648/j.acm.20130202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.11},
  abstract = {Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.},
 year = {2013}
}

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TY  - JOUR
T1  - A Classic New Method to Solve Quartic Equations
AU  - Amir Fathi
AU  - Nastaran Sharifan
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.11
DO  - 10.11648/j.acm.20130202.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 24
EP  - 27
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.11
AB  - Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.
VL  - 2
IS  - 2
ER  -

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Author Information

Amir Fathi

Department of Electrical Engineering, Urmia branch, Islamic Azad University, Urmia, Iran
Nastaran Sharifan

Department of law, Varamin-Pishva branch, Islamic Azad University, Varamin, Pishva, Iran

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Plain Text BibTeX RIS

APA Style

Amir Fathi, Nastaran Sharifan. (2013). A Classic New Method to Solve Quartic Equations. Applied and Computational Mathematics, 2(2), 24-27. https://doi.org/10.11648/j.acm.20130202.11

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ACS Style

Amir Fathi; Nastaran Sharifan. A Classic New Method to Solve Quartic Equations. Appl. Comput. Math. 2013, 2(2), 24-27. doi: 10.11648/j.acm.20130202.11

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AMA Style

Amir Fathi, Nastaran Sharifan. A Classic New Method to Solve Quartic Equations. Appl Comput Math. 2013;2(2):24-27. doi: 10.11648/j.acm.20130202.11

Copy | Download

@article{10.11648/j.acm.20130202.11,
  author = {Amir Fathi and Nastaran Sharifan},
  title = {A Classic New Method to Solve Quartic Equations},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {24-27},
  doi = {10.11648/j.acm.20130202.11},
  url = {https://doi.org/10.11648/j.acm.20130202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.11},
  abstract = {Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - A Classic New Method to Solve Quartic Equations
AU  - Amir Fathi
AU  - Nastaran Sharifan
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.11
DO  - 10.11648/j.acm.20130202.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 24
EP  - 27
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.11
AB  - Polynomials of high degrees often appear in many problems such as optimization problems. Equations of the fourth degree or so called quartics are one type of these polynomials. In this paper we give a new Classic method for solving a fourth degree polynomial equation (Quartic). We will show how the quartic formula can be presented easily at the precalculus level.
VL  - 2
IS  - 2
ER  -

Copy | Download