Solution of Cubic and Quartic Equations

Marco Riccardi

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 117-122
  • ISSN: 1426-2630

Abstract

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In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].

How to cite

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Marco Riccardi. "Solution of Cubic and Quartic Equations." Formalized Mathematics 17.2 (2009): 117-122. <http://eudml.org/doc/267002>.

@article{MarcoRiccardi2009,
abstract = {In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].},
author = {Marco Riccardi},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {117-122},
title = {Solution of Cubic and Quartic Equations},
url = {http://eudml.org/doc/267002},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Marco Riccardi
TI - Solution of Cubic and Quartic Equations
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 117
EP - 122
AB - In this article, the principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan's solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coefficients are also presented [5].
LA - eng
UR - http://eudml.org/doc/267002
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. 
  3. [3] Yuzhong Ding and Xiquan Liang. Solving roots of polynomial equation of degree 2 and 3 with complex coefficients. Formalized Mathematics, 12(2):85-92, 2004. 
  4. [4] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  5. [5] G.A. Korn and T.M. Korn. Mathematical Handbook for Scientists and Engineers. Dover Publication, New York, 2000. Zbl0121.00103
  6. [6] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. 
  7. [7] Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9(3):455-460, 2001. 
  8. [8] Jan Popiołek. Quadratic inequalities. Formalized Mathematics, 2(4):507-509, 1991. 
  9. [9] Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991. 
  10. [10] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990. 
  11. [11] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  12. [12] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998. 

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