Cubic Formula | cubic equation formula
Thecubicformulaistheclosed-formsolutionforacubicequation[1],i.e.,therootsofacubicpolynomial[2].Ageneralcubicequation[3]isoftheform(1)(thecoefficient[4]ofmaybetakenas1withoutlossofgeneralitybydividingtheentireequationthroughby).TheWolframLanguage[5]cansolvecubicequationsexactlyusingthebuilt-incommandSolve[6][a3x3+a2x2+a1x+a0==0,x].ThesolutioncanalsobeexpressedintermsoftheWolframLanguage[7]algebraicrootobjectsbyfirstissuingSetOptions[8][Roots,Cubics->False].Thesolutiontothecubic(aswellasthe...
The cubic formula is the closed-form solution for a cubic equation[1], i.e., the roots of a cubic polynomial[2]. A general cubic equation[3] is of the form
(1)
(the coefficient[4] of may be taken as 1 without loss of generality by dividing the entire equation through by ). The Wolfram Language[5] can solve cubic equations exactly using the built-in command Solve[6][a3 x3 + a2 x2 + a1 x + a0 == 0, x]. The solution can also be expressed in terms of the Wolfram Language[7] algebraic root objects by first issuing SetOptions[8][Roots, Cubics -> False].
The solution to the cubic (as well as the quartic[9]) was published by Gerolamo Cardano (1501-1576) in his treatise Ars Magna. However, Cardano was not the original discoverer of either of these results. The hint for the cubic had been provided by Niccolò Tartaglia, while the quartic had been solved by Ludovico Ferrari. However, Tartaglia himself had probably caught wind of the solution from ...