What is the quadratic formula?

The quadratic formula is x = (−b ± √(b² − 4ac)) / 2a. It solves any equation of the form ax² + bx + c = 0 by directly computing all roots, regardless of whether they are real or complex.

What does the discriminant tell you?

The discriminant is b² − 4ac. If it is positive, the equation has two distinct real roots. If it is zero, there is exactly one real root (a repeated root). If it is negative, the equation has two complex (imaginary) roots and the parabola does not cross the x-axis.

Advertisement (728x90)

✏️

📐 Math

Quadratic Equation Calculator

Solve any quadratic equation instantly. Handles two real roots, one root, and complex (imaginary) roots using the quadratic formula.

⚡ Instant 🆓 Free 🔒 Private

quadratic equation discriminant roots algebra math

Solve: ax² + bx + c = 0

The Quadratic Formula Explained

The Formula

For any equation of the form ax² + bx + c = 0, the roots are found by: x = (−b ± √(b² − 4ac)) / 2a

The Discriminant (Δ = b² − 4ac)

Δ > 0: Two distinct real roots. The parabola crosses the x-axis at two points.
Δ = 0: One repeated real root. The parabola just touches the x-axis (vertex on axis).
Δ < 0: Two complex (imaginary) roots. The parabola never crosses the x-axis.

Practical Applications

Quadratic equations model projectile motion, area optimization, revenue maximization in economics, and signal processing in electrical engineering — making this formula one of the most widely applied in all of mathematics.