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Resolveur d'Equation du Second Degre.

Resoudre des equations quadratiques ax² + bx + c = 0

Calcul sur l'appareilSans inscription
01

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Les résultats se mettent à jour pendant la saisie.

Resoudre : ax² + bx + c = 0

1x² -5x + 6 = 0

Analyse du Discriminant

Discriminant1.0000
Nature des Racines✓ Deux Racines Reelles Distinctes

Solution x1

3.0000

Solution x2

2.0000

Proprietes de la Parabole

Sommet(2.5000, -0.2500)
Axe de Symetriex = 2.5000
Ordonnee a l'origine(0, 6)
Ouverture↑ Vers le haut (Minimum)

Comprendre les Equations du Second Degre

Formule Quadratique : x = (-b ± √(b² - 4ac)) / 2a. Cette formule resout toute equation quadratique ax² + bx + c = 0.
Discriminant (Δ) : La valeur Δ = b² - 4ac determine la nature des racines :
  • • Δ > 0 : Deux racines reelles distinctes (la parabole coupe l'axe des X deux fois)
  • • Δ = 0 : Une racine reelle double (la parabole touche l'axe des X une fois)
  • • Δ < 0 : Deux racines complexes (la parabole ne touche pas l'axe des X)
Forme Sommet : Le sommet represente le point minimum (a > 0) ou maximum (a < 0) de la parabole. Il est situe en x = -b/(2a).

Cite this calculator

Canonical URL: https://mathify.one/fr/math/quadratic

Cite as: Mathify. (n.d.). Resolveur d'Equation du Second Degre. https://mathify.one/fr/math/quadratic

Use Cases

Homework and Exam Preparation

Quickly verify your manual solutions to quadratic equations, check your work, and understand the step-by-step process.

Example: Solve x² - 5x + 6 = 0 to get roots 2 and 3.

Engineering and Physics Calculations

Find roots of quadratic equations that arise in projectile motion, circuit analysis, and optimization problems.

Example: Determine the time when a projectile hits the ground using h = -4.9t² + 20t + 1.

Frequently Asked Questions

How do I use the Quadratic Solver?
Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The solver will compute the roots using the quadratic formula and display the solutions, including complex roots if the discriminant is negative.
What if the discriminant is negative?
If the discriminant (b² - 4ac) is negative, the equation has no real roots. The solver will show the complex roots in the form of a + bi, where i is the imaginary unit.
Can the solver handle a = 0?
If a = 0, the equation is not quadratic but linear. The solver will indicate that the equation is not quadratic and may not provide a solution. Ensure a ≠ 0 for a valid quadratic equation.

Tips & Common Mistakes

Tips

  • Ensure the equation is in standard form ax² + bx + c = 0 before entering coefficients.
  • Double-check the signs of b and c; a common error is entering a negative b as positive.
  • Use the discriminant (b² - 4ac) to predict the nature of roots: positive for two real, zero for one real, negative for complex.
  • If a = 0, the equation is linear, not quadratic, so the solver may not work correctly.

Common Mistakes to Avoid

  • Entering coefficients in the wrong order (e.g., swapping a and c).
  • Forgetting to include the sign of the coefficient (e.g., entering 5 instead of -5 for b).
  • Assuming the solver can handle a = 0; it's designed for quadratic equations only.

Last updated: August 13, 2026