Cubic function

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

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:

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).

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.