Quadratic Equations
12-3The Quadratic Formula
Overview
For ax² + bx + c = 0 (a ≠ 0): x = [−b ± √(b² − 4ac)] / (2a).
Key ideas
- Works for ANY quadratic.
- Compute the discriminant b² − 4ac first.
- Simplify the radical.
Worked examples
Example 1
Problem. Solve x² − 5x + 6 = 0 with the formula.
Solution. x = [5 ± √(25 − 24)]/2 = (5 ± 1)/2 → x = 3 or 2.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve x² + 3x − 10 = 0.
- 2.
Solve 2x² + 5x − 3 = 0.
- 3.
Solve x² − 4x + 1 = 0.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve using the quadratic formula: 2x² + 5x − 3 = 0.
- 2.
Solve using the quadratic formula: x² − 3x + 1 = 0.