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:

4 x 2 – 12 = 0, x 2 + 5 x = 0, x 2 = 36 .

Back