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Solve quadratic equations (ax² + bx + c = 0) with roots, discriminant, and parabola vertex.
Must not be 0 for a quadratic equation.
Two distinct real roots
Analysis for 1x² + -5x + 6 = 0
| Property | Value |
|---|---|
| Equation | 1x² - 5x + 6 = 0 |
| Roots | x₁ = 3.000, x₂ = 2.000 |
| Discriminant | 1 |
| Nature of Roots | Two distinct real roots |
| Parabola Vertex | (2.50, -0.25) |
| Y-Intercept | (0, 6) |
Standard quadratic formula with discriminant Δ determining the nature of roots.
x² - 5x + 6 = 0
Δ = (-5)² - 4(1)(6) = 25 - 24 = 1. x = (5 ± √1) / 2 = (5 ± 1) / 2
x₁ = 3, x₂ = 2
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