Quadratic Equations

Quadratic Equations

A quadratic equation has the form:

ax² + bx + c = 0

Three Methods to Solve

1. Factoring

Best for simple equations where factors are integers.

Example: x² - 5x + 6 = 0

• Factor: (x - 2)(x - 3) = 0
• Solutions: x = 2 or x = 3

2. Quadratic Formula

Works for all quadratic equations:

x = (-b ± √(b² - 4ac)) / 2a

3. Completing the Square

Useful for deriving the quadratic formula or when coefficient of x² is 1.

The Discriminant

The value b² - 4ac tells you about the solutions:

• Positive: Two real solutions
• Zero: One real solution (double root)
• Negative: No real solutions (complex roots)