The solutions of ax² + bx + c = 0 can always be found using the quadratic formula.
x = ( −b ± √(b² − 4ac) ) ÷ 2a
📘 Example ①
Solve x² + 3x − 1 = 0 using the quadratic formula.
Answer:a=1, b=3, c=−1. x = (−3 ± √(9+4)) / 2 = (−3 ± √13) / 2
Solve x² + 3x − 1 = 0 using the quadratic formula.
Answer:a=1, b=3, c=−1. x = (−3 ± √(9+4)) / 2 = (−3 ± √13) / 2
💡 Key Points
- Check the coefficients a, b, and c before substituting
- If b² − 4ac (the discriminant) is less than 0, there are no real solutions
- A powerful method when factoring is not possible
Practice Problem
- Solve x² − 4x + 1 = 0 using the quadratic formula.
Answer and Explanation
- Answer:x = (4 ± √12) / 2 = 2 ± √3.