A cubic polynomial is a polynomial of polynomial degree 3. A univariate polynomial of
this polynomial degree has the form 
with 
. An equation involving a
cubic polynomial is called a cubic equation. A
closed-form solution known as the cubic formula
exists for the solutions of an arbitrary cubic equation.
Dividing by the leading coefficient gives a monic polynomial, which can be written as
 |
For real coefficients, the polynomial discriminant
 |
determines the number of real roots. If 
, there are three distinct real
roots. If 
,
there is one real root and a nonreal complex
conjugate pair. If 
,
all three roots are real,
counting multiplicity, and at least two coincide
(Trott 2006). The root is triple iff 
and 
, in which case 
. Otherwise, when 
, there is one double root and one
simple root.
