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

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

Given a polynomial equation x 3 + ax 2 + 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 x 3 + px + q = 0 where Therefore, in order to solve a polynomial equation of degree 3, it...

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Veröffentlicht in:Mathematical gazette 2023-11, Vol.107 (570), p.438-444
Hauptverfasser: Liao, Hsin-Chieh, Saul, Mark, Shiue, Peter J.-S
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Shiue, Peter J.-S
description Given a polynomial equation x 3 + ax 2 + 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 x 3 + px + q = 0 where Therefore, in order to solve a polynomial equation of degree 3, it is sufficient to solve equations of the form x 3 + px + q = 0.
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title Revisiting the general cubic: a simplification of Cardano's solution
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