Quadratic Equation Solver
Enter a, b, and c from ax² + bx + c = 0 to find the roots.
About the Quadratic Equation Solver
The Quadratic Solver finds the roots of an equation of the form ax² + bx + c = 0. Enter the coefficients a, b and c and see the discriminant and the solutions, whether real or complex.
The discriminant b² − 4ac decides the type of roots. If it is positive there are two different real roots, if zero there is one repeated real root, and if negative there are two complex roots, shown with a real part and an imaginary part. The roots are calculated with the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The coefficient a cannot be zero, otherwise the equation is linear.
How to use it
- Enter a, b and c.
- Read the discriminant.
- Read the roots.
- Substitute a root back into the equation to check it.
Tips and good to know
- Rearrange the equation to the standard form first.
- Roots are shown to four decimal places.
- The sum of the roots is −b/a and the product is c/a.
Frequently asked questions
What if a is zero?
The equation is not quadratic; solve it as a linear equation.
What are complex roots?
Roots involving the imaginary unit i, when the parabola does not cross the x-axis.
Can I get exact surds?
The tool gives decimal values.