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An alternative formula for the cubic 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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Extract

Consider the general cubic equation:

$${x^3} + a{x^2} + bx + c = 0.$$

A change of variable: x = z + t leads to: (1)

$${z^3} + (3t + a){z^2} + (3{t^2} + 2at + b)z + ({t^3} + {at^2} + bt + c) = 0.$$

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 474 - 479
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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References

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