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is called the discriminant of the quadratic equation,
. Note that this is the expression under the radical in the quadratic equation.
is the symbol for the discriminant, so
If
then there is a single root to the quadratic with multiplicity of 2 and that root is
. The term multiplicity of 2 arises from the fact that every quadratic can be represented as two factors:
where
and
can be either complex or real numbers. In the case of
,
.
If
then there are two distinct real number roots.
If
then there is a conjugate pair of complex roots of the form
where
is the imaginary number defined by
