一元二次方程计算器 — 公式

How to Use the Quadratic Formula

Formula

x = (-b ± √(b² - 4ac)) / (2a)

For the equation ax² + bx + c = 0

Discriminant (Δ = b² - 4ac)

  • Δ > 0: Two distinct real roots
  • Δ = 0: One repeated real root
  • Δ < 0: Two complex roots (no real solutions)

    • Vertex

    The vertex of the parabola is at x = -b/(2a), y = f(-b/(2a)).

    计算示例

    Solve x² - 5x + 6 = 0 (a=1, b=-5, c=6).

    1. Discriminant = (-5)² - 4(1)(6) = 25 - 24 = 1
    2. Since Δ > 0, there are two distinct real roots
    3. x₁ = (5 + √1) / 2 = 6 / 2 = 3
    4. x₂ = (5 - √1) / 2 = 4 / 2 = 2
    5. Vertex: x = 5/2 = 2.5, y = (2.5)² - 5(2.5) + 6 = -0.25