Quadratic equation
Quadratic equation. Reduced quadratic equation.
Nonreduced 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
nonreduced 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 .
Back
