An equation in the form ax² + bx + c = 0（a ≠ 0）is called a quadratic equation. It often has two solutions (values of x).
📘 Example ①
Determine whether x = 3 is a solution of x² − 2x − 3 = 0.
Answer:3² − 2×3 − 3 = 9 − 6 − 3 = 0 ✓ It is a solution.
Determine whether x = 3 is a solution of x² − 2x − 3 = 0.
Answer:3² − 2×3 − 3 = 9 − 6 − 3 = 0 ✓ It is a solution.
💡 Key Points
- The form ax² + bx + c = 0 (make the right side = 0)
- If substitution gives 0, it is a solution
- A quadratic equation has at most two solutions
Practice Problems
- Determine whether x = −1 is a solution of x² + x = 0.
- Which of the following is a quadratic equation? (A) 2x + 3 = 0 (B) x² − 4 = 0 (C) x³ = 1
Answers and Explanations
- Answer:It is a solution. (−1)² + (−1) = 1 − 1 = 0 ✓.
- Answer:(B). An equation with an x² term is a quadratic equation.