Solve any quadratic equation of the form ax² + bx + c = 0. Enter a, b and c to get both roots and the discriminant.
How the quadratic equation solver works
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac tells you the type of roots: positive gives two real roots, zero gives one repeated root, and negative gives two complex roots.
Example
For x² − 3x + 2 = 0 the discriminant is 1, so the roots are x = 2 and x = 1.
Frequently asked questions
What does the discriminant tell me?
Its sign shows whether the equation has two real roots, one repeated root or two complex roots.
What if a is zero?
Then the equation is linear, not quadratic, and has a single solution x = −c ÷ b.
Can the roots be complex?
Yes. When the discriminant is negative the roots are shown in the form p ± qi.