## ::Cubic function

### ::concepts

Roots::cubic Equation::first Complex::title ''x''::delta Three::solution Which::method

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In algebra, a **cubic function** is a function of the form

- <math>f(x)=ax^3+bx^2+cx+d,\,</math>

where *a* is nonzero. In other words, a cubic function is defined by a polynomial of degree three.

Setting *ƒ*(*x*) = 0 produces a **cubic equation** of the form:

- <math>ax^3+bx^2+cx+d=0.\,</math>

Usually, the coefficients *a*, *b*, *c*, *d* are real numbers. However much of the theory of cubic equations for real coefficients applies to other types of coefficients (such as complex ones).<ref>Exceptions include fields of characteristic 2 and 3.</ref>

Solving the cubic equation is equivalent to finding the particular value (or values) of *x* for which *ƒ*(*x*) = 0. There are various methods to solve cubic equations. The solutions of a cubic equation, also called roots of the cubic function, can always be found algebraically. (This is also true of a quadratic or quartic (fourth degree) equation, but no higher-degree equation, by the Abel–Ruffini theorem). The roots can also be found trigonometrically. Alternatively, one can find a numerical approximation of the roots in the field of the real or complex numbers such as by using root-finding algorithms like Newton's method.

**Cubic function sections**

Intro History Critical points of a cubic function Roots of a cubic function Collinearities Applications See also Notes References External links

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