Quadratic Equation Solver
Solve ax² + bx + c = 0 with step-by-step working and real/complex roots.
ax² + bx + c = 0
How to Use
- Step 1: Enter coefficients a, b, and c for your equation ax² + bx + c = 0.
- Step 2: The discriminant and roots are computed instantly with full step-by-step working.
- Step 3: Complex roots are shown in p ± qi format when D < 0.
About Quadratic Equation Solver
The quadratic formula is one of the fundamental tools in algebra. Given a quadratic equation ax² + bx + c = 0, this solver uses the quadratic formula x = (−b ± √(b² − 4ac)) / (2a) to find the roots. The key quantity is the discriminant D = b² − 4ac, which determines the nature of the solutions.
When D is positive, there are two distinct real roots. When D is exactly zero, there is one repeated real root. When D is negative, the square root of a negative number is imaginary, giving two complex conjugate roots in the form p ± qi where q = √|D| / (2a).
The step-by-step display helps students learn the process, not just the answer. All calculations are performed in your browser with no data sent to any server.
You may also find our Scientific Calculator and Matrix Calculator helpful.
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0. It can have 0, 1, or 2 real solutions.
What is the discriminant?
D = b² − 4ac. If D > 0: two real roots. If D = 0: one repeated root. If D < 0: two complex roots.
What are complex roots?
When D < 0, roots are complex numbers with real and imaginary parts, shown as p ± qi.
What if a = 0?
The equation becomes linear (bx + c = 0), not quadratic. The solver requires a ≠ 0.
Can I enter decimal coefficients?
Yes — a, b, and c can be any real numbers including decimals and negatives.