An equation in the form ax² + bx + c = 0 is called a quadratic equation. If AB = 0, use the fact that A = 0 or B = 0 to solve it.
Factor the left side, then set each factor equal to 0 to find the solutions.
Example ①
Solve x² - 5x + 6 = 0.
Solution:(x - 2)(x - 3) = 0, so x = 2 or 3
Solve x² - 5x + 6 = 0.
Solution:(x - 2)(x - 3) = 0, so x = 2 or 3
Example ②
Solve 2x² - 5x - 3 = 0.
Solution:(2x + 1)(x - 3) = 0, so x = -1/2 or 3
Solve 2x² - 5x - 3 = 0.
Solution:(2x + 1)(x - 3) = 0, so x = -1/2 or 3
Key Points
- Make the right side 0 before factoring
- AB = 0 ⇒ A = 0 or B = 0
- If integer solutions cannot be obtained, use the quadratic formula
Practice Problems
- Solve x² + 3x - 10 = 0.
- Solve 3x² - 7x + 2 = 0.
Solutions and Explanations
- Solution:x = 2, -5. (x - 2)(x + 5) = 0.
- Solution:x = 2, 1/3. (3x - 1)(x - 2) = 0.