Solving Quadratic Equations
The formula that solves every quadratic equation, including those with complex roots.
The Quadratic Formula
For an equation $ax^2 + bx + c = 0$:
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$The Discriminant
The value $D = b^2 - 4ac$ tells us the nature of the roots:
| Discriminant | Nature of Roots |
|---|---|
| $D > 0$ | Two distinct real roots |
| $D = 0$ | Two equal real roots |
| $D < 0$ | Two complex (conjugate) roots |
Lesson 9 of 27