Quadratic Formula Calculator

Solve quadratic equations using the quadratic formula. Enter coefficients a, b, and c for the equation ax² + bx + c = 0.

ax² + bx + c = 0

Coefficient a:

Coefficient b:

Coefficient c:

How to Use

Enter the coefficients a, b, and c from your quadratic equation
Click "Solve Equation" to find the roots
Use "Load Example" to see a sample calculation
The calculator shows the nature of roots and discriminant

What is a Quadratic Equation?

A quadratic equation is a second-degree polynomial equation in a single variable x, with the general form ax² + bx + c = 0, where a ≠ 0.

Examples

x² - 5x + 6 = 0 → x = 2, x = 3
x² - 4x + 4 = 0 → x = 2 (repeated root)
x² + 1 = 0 → x = ±i (complex roots)

Applications

Physics: Projectile motion, parabolic trajectories
Engineering: Structural analysis, optimization
Economics: Cost functions, profit maximization
Geometry: Area and volume calculations