📐 Quadratic Equation Solver
x² − 3x + 2 = 0
x₁ = 2, x₂ = 1
Two distinct real roots (discriminant > 0)
- Discriminant (b² − 4ac)
- 1
- Vertex
- (1.5, −0.25)
- Axis of symmetry
- x = 1.5
| Parabola opens | Upward (minimum at vertex) |
| y-intercept | (0, 2) |
| Sum of roots (−b/a) | 3 |
| Product of roots (c/a) | 2 |
Step by step
- Identify the coefficients: a = 1, b = −3, c = 2
- Discriminant: D = b² − 4ac = (−3)² − 4 × 1 × 2 = 1
- Quadratic formula: x = (−b ± √D) ÷ 2a = (3 ± √1) ÷ 2
- Roots: x₁ = 2, x₂ = 1
- Vertex: x = −b ÷ 2a = 1.5, y = c − b² ÷ 4a = −0.25