Solving Quadratic Equations

Standard Form

$ax^2 + bx + c = 0$

Method 1: Factoring

Example: $x^2 + 5x + 6 = 0$

Factor: $(x + 2)(x + 3) = 0$

Solutions: $x = -2$ or $x = -3$

Method 2: Square Root Method

For $x^2 = k$: $x = \pm\sqrt{k}$

Method 3: Quadratic Formula

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

The discriminant $b^2 - 4ac$ determines number of solutions:

• Positive: 2 real solutions
• Zero: 1 real solution
• Negative: no real solutions