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Revisiting the general cubic: a simplification of Cardano's solution

Published online by Cambridge University Press:  11 October 2023

Hsin-Chieh Liao ,
Mark Saul  and
Peter J.-S Shiue
Hsin-Chieh Liao
Affiliation:
Department of Mathematics, University of Miami, Florida 33146, USA e-mail: h.liao@math.miami.edu
Mark Saul
Affiliation:
Nine Nine Cultural and Educational Foundation, 9F, No. 300, Sec 3. Roosevelt Road, Zhongzheng Dist., Taipei City 10900, Taiwan e-mail: marksaul@earthlink.net
Peter J.-S Shiue
Affiliation:
Department of Mathematical Sciences, University of Nevada, Las Vegas NV 89154-4020, USA e-mail: shiue@unlv.nevada.edu
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Extract

Given a polynomial equation x3 + ax2 + bx + c = 0 of degree 3 with real coefficients, we may translate the variable by replacing x with x − to make the quadratic term vanish. We then obtain a simpler equation x3 + px + q = 0 where Therefore, in order to solve a polynomial equation of degree 3, it is sufficient to solve equations of the form x3 + px + q = 0.

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 570 , November 2023 , pp. 438 - 444
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Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

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References

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