Quadratic formula

In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.

Given a general quadratic equation of the form

${\displaystyle ax^{2}+bx+c=0}$

whose discriminant ${\displaystyle b^{2}-4ac}$ is positive (with x representing an unknown, a, b and c representing constants with a ≠ 0), the quadratic formula is:

${\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }$

where the plus–minus symbol "±" indicates that the quadratic equation has two solutions.[1] Written separately, they become:

${\displaystyle x_{1}={\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}}\quad {\text{and}}\quad x_{2}={\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}}$

Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax² + bx + c, crosses the x-axis.[2]

As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola,[3] and the number of real zeros the quadratic equation contains.[4]