# Quadratic equation

*Quadratic equation. Reduced quadratic equation.*

Non-reduced quadratic equation. Pure quadratic equation.

Non-reduced quadratic equation. Pure quadratic equation.

**
A quadratic equation
**
is an algebraic equation of the second degree:

*ax*

^{ 2 }

*+ bx + c = 0*,

*(1)*

where
*
a, b, c –
*
the given numerical or literal coefficients
*
, x –
*
an unknown.

If
*
a =
*
0, then this equation becomes a linear one. Therefore, we’ll consider here only
*
a
≠
*
0. So, it is possible to divide all terms of the equation by
*
a
*
and then we receive:

*x*

^{ 2 }

*+ px + q = 0 ,*(2)

where
*
p=b/a, q=c/a
*
. This quadratic equation is called a
*
reduced
*
one. The equation (1) is called a
*
non-reduced
*
quadratic equation. If
*
b
*
or
*
c
*
(or both) is
equal to zero, then this equation is called a
*
pure
*
one. The examples of pure quadratic equations are following:

*x*

^{ 2 }– 12 = 0,

*x*

^{ 2 }+ 5

*x*= 0,

*x*

^{ 2 }= 36 .