Quadratische-Gleichung-Löser — Formel
## How to Solve a Quadratic Equation
### Quadratic Formula
**x = (-b ± sqrt(b² - 4ac)) / (2a)**
For the equation ax² + bx + c = 0:
1. Calculate the **discriminant**: D = b² - 4ac
2. If D > 0: two distinct real roots
3. If D = 0: one repeated real root
4. If D < 0: no real roots (complex roots)
### Vertex
The vertex of the parabola is at x = -b/(2a), y = c - b²/(4a).
### Quadratic Formula
**x = (-b ± sqrt(b² - 4ac)) / (2a)**
For the equation ax² + bx + c = 0:
1. Calculate the **discriminant**: D = b² - 4ac
2. If D > 0: two distinct real roots
3. If D = 0: one repeated real root
4. If D < 0: no real roots (complex roots)
### Vertex
The vertex of the parabola is at x = -b/(2a), y = c - b²/(4a).
Lösungsbeispiel
Solve x² - 5x + 6 = 0.
- D = (-5)² - 4(1)(6) = 25 - 24 = 1
- x₁ = (5 + √1) / 2 = 6/2 = 3
- x₂ = (5 - √1) / 2 = 4/2 = 2
- Roots are x = 3 and x = 2