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    ProofWiki
    https://proofwiki.org › wiki › Cardano's_Formula

    Cardano's Formula - ProofWiki

    • Let PP be the cubic equation: 1. ax3+bx2+cx+d=0ax3+bx2+cx+d=0 with a≠0a≠0 Then PPhas solutions: where: where: The expression D=Q3+R2D=Q3+R2 is called the discriminantof t… See more

    Proof

    First the cubic is depressed, by using the Tschirnhaus Transformation: 1. … See more

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    Also Presented as

    Cardano's Formulacan also be presented in the following form: Let P be the cubic equation: 1. x3+a2x2+a1x+a0=0 Then Phas solutions: where: where: See more

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    Also Known as

    Cardano's Formula is also sometimes seen referred to as Cardan's Formula, from the English form of Cardano's name, Jerome Cardan. Some use the term Cardano's Method. So… See more

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    Examples

    Example: x3−15x−4
    1. x3−15x−4=0 has solutions x=4, x=−2+√3 and x=−2−√3. See more

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    Historical Note

    Cardano's Formula (in an incomplete form) was first published by Gerolamo Cardano in 1545, in his Artis Magnae, Sive de Regulis Algebraicis. He learned the technique from Niccolò Fo… See more

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    Where can I find images of Gerolamo Cardano?
    Online Galleries, History of Science Collections, University of Oklahoma Libraries High-resolution images of works by and/or portraits of Gerolamo Cardano in .jpg and .tiff format. Forster, E.M. 'Cardan' in Abinger Harvest (1936).
    en.wikipedia.org