Solveur d'Équation Quadratique — Formule

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).

Exemple Résolu

Solve x² - 5x + 6 = 0.

  1. D = (-5)² - 4(1)(6) = 25 - 24 = 1
  2. x₁ = (5 + √1) / 2 = 6/2 = 3
  3. x₂ = (5 - √1) / 2 = 4/2 = 2
  4. Roots are x = 3 and x = 2