The quadratic formula gives the roots of a quadratic equation
 |
(1)
|
with 
as
 |
(2)
|
An alternate form, valid when the denominator is nonzero, is given by
 |
(3)
|
For a quadratic equation with leading coefficient 1,
 |
(4)
|
the quadratic formula becomes the 
formula (Kucherenko 2007),
 |
(5)
|
This form follows by dividing the general quadratic equation by 
and setting 
and 
.
For real 
and 
, the roots are real iff 
.
