The Quadratic Formula

1 / 4

Solving Method

When factoring is hard, this formula always works. The discriminant tells you how many solutions exist.

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

Discriminant $b^{2}-4ac$ determines number of real roots

$b^{2} - 4 a c > 0$

Two real roots

Parabola crosses $x$ -axis twice

$b^{2} - 4 a c = 0$

One real root

Parabola just touches $x$ -axis

$b^{2} - 4 a c < 0$

No real roots

Parabola doesn't cross $x$ -axis