Quadratic Equation Solver
Solve ax² + bx + c = 0 with discriminant, real or complex roots, vertex, step-by-step working and a graph.
About Quadratic Equation Solver
This quadratic equation solver online solves any equation of the form ax² + bx + c = 0. Enter the coefficients a, b and c and it works out the discriminant, tells you whether the roots are real and different, real and equal or complex, and gives the roots with full step-by-step working using the quadratic formula.
It also shows the vertex and plots the parabola, so you can check the roots visually where the curve meets the x-axis. It is a free quadratic equation solver with steps for students checking homework or preparing for exams, with nothing to install or sign up for.
How to use Quadratic Equation Solver
- Enter the coefficients a, b and c of ax² + bx + c = 0.
- Read the discriminant and the nature of the roots.
- Follow the steps and check the roots on the graph.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a. In India it is also called the Sridharacharya formula.
What does the discriminant tell me?
D = b² − 4ac. If D > 0 there are two distinct real roots, if D = 0 one repeated real root, and if D < 0 two complex conjugate roots.
What if a = 0?
Then the equation is linear (bx + c = 0), with the single root x = −c/b. The solver handles this case too.
How do I solve a quadratic equation?
Put the equation in the form ax² + bx + c = 0 and apply x = (−b ± √(b² − 4ac)) ÷ 2a. The solver shows each step of this working.
Can it solve equations with complex roots?
Yes. When the discriminant is negative, the solver gives the two complex roots in the form p ± qi.
What is the vertex of a quadratic?
It is the turning point of the parabola, at x = −b ÷ 2a. The solver shows its coordinates on the graph.
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