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A novel method to solve the quartic equation

Published online by Cambridge University Press:  12 October 2022

Abdel Missa  and
Chrif Youssfi
Abdel Missa
Affiliation:
Department of Finance, Jacksonville University, 2800 University Blvd N, Jacksonville FL 32211 USA e-mail: amissa@ju.edu
Chrif Youssfi
Affiliation:
MarketCipher Partners, Quantitative Research, Rabat, Morocco e-mail: cyoussfi@market-cipher.com
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The first solution to the quartic equation is attributed to Lodovico Ferrari, a student of Geralamo Cardano. The solution was published alongside the solution of the cubic in Cardano’s book Ars Magna [1]. In this Article, we introduce a new canonical form to simplify the derivation of the roots of the equation (1)

$${z^4} + {z^3} + f{z^2} + g = 0\quad \textrm{with}\quad f,g \in \mathbb{R}.$$

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 480 - 486
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

References

Cardano, Girolamo, Ars Magna (1545).Google Scholar