Quadratic
equation
Quadratic equation. Reduced 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:
4x 2 – 12 =
0, x 2 + 5x =
0, x 2 = 36 .
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