Cubic equation | cubic equation formula
Polynomialequationofdegree3Thisarticleisaboutcubicequationsinonevariable.Forcubicequationsintwovariables,seecubicplanecurve.Graphofacubicfunctionwith3realroots(wherethecurvecrossesthehorizontalaxisaty=0).Thecaseshownhastwocriticalpoints.Herethefunctionisf(x)=(x3+3x2−6x−8)/4.Inalgebra,acubicequationinonevariableisanequationoftheformax3+bx2+cx+d=0{displaystyleax{3}+bx{2}+cx+d=0}inwhichaisnonzero.Thesolutionsofthisequationarecalledrootsofthecubicfunctiondefinedbytheleft-handsideoftheequation.If...
Polynomial equation of degree 3
This article is about cubic equations in one variable. For cubic equations in two variables, see cubic plane curve. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0). The case shown has two critical points. Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4.In algebra, a cubic equation in one variable is an equation of the form
ax3+bx2+cx+d=0{displaystyle ax{3}+bx{2}+cx+d=0}in which a is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means:
The coefficients do not need to be real numbers. Much of what is covered below is valid for coefficients in any fiel...