Quadratic equations. Root formula

A quadratic equation $ax^2 + bx + c = 0$ ($a \neq 0$) can be solved for $x$ using the quadratic formula:

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

The expression under the square root, $b^2 - 4ac$, is called the discriminant. It determines the nature of the roots.

Important properties

• If $b^2 - 4ac > 0$, there are two distinct real roots.

• If $b^2 - 4ac = 0$, there is one real root (a repeated root).

• If $b^2 - 4ac < 0$, there are two complex roots.

• The sum of the roots is $-b/a$ and the product is $c/a$.