📐 Quadratic Formula Calculator
Solve quadratic equations step by step
Solve ax² + bx + c = 0
How the Quadratic Formula Works
Formula
x = (−b ± √(b² − 4ac)) / 2a
- 1Enter the coefficients a, b, and c from your equation ax² + bx + c = 0.
- 2The discriminant (b² − 4ac) is calculated first.
- 3If the discriminant is positive, there are two distinct real roots.
- 4If the discriminant is zero, there is exactly one real root.
- 5If the discriminant is negative, the roots are complex numbers.
About Quadratic Formula Calculator
Solve any quadratic equation using the quadratic formula. Enter coefficients a, b, and c to find both real and complex roots with step-by-step solution breakdown.
Frequently Asked Questions
What is the discriminant?
The discriminant is b² − 4ac. It determines the nature of the roots: positive means two real roots, zero means one repeated root, and negative means two complex (imaginary) roots.
Can the quadratic formula solve all quadratic equations?
Yes. The quadratic formula works for every quadratic equation of the form ax² + bx + c = 0, as long as a is not zero. If a is zero, the equation is linear, not quadratic.
What are complex roots?
Complex roots occur when the discriminant is negative. They involve the imaginary unit i (where i² = −1) and always come in conjugate pairs, such as 2 + 3i and 2 − 3i.