Quadratic Formula Calculator

What Is the Quadratic Formula?

The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It solves any quadratic equation of the form ax² + bx + c = 0, where a ≠ 0. The expression under the square root, b² - 4ac, is called the discriminant and determines the nature of the roots.

How Does the Discriminant Work?

If the discriminant is positive, the equation has two distinct real roots. If it equals zero, there is exactly one repeated real root. If the discriminant is negative, the equation has two complex conjugate roots.

When to Use the Quadratic Formula

Use the quadratic formula when factoring is difficult or impossible. It works for every quadratic equation, including those with irrational or complex roots. For simpler equations, factoring or completing the square may be faster.

For more complex math problems, try our AI Quadratic Equation Solver or download Solver AI for camera scanning and detailed explanations.