How to solve a quadratic equation
A quadratic equation has the form ax squared plus bx plus c equals zero. The quadratic formula finds its solutions, the values of x, for any a, b and c. This calculator applies the formula and returns the roots, including whether they are real or complex. Just enter the three coefficients.
The quadratic formula
x = (-b plus or minus the square root of (b squared - 4ac)) / (2a). The part under the root, b squared - 4ac, is the discriminant; if it is negative, the roots are complex.
Worked example
For x squared - 3x + 2 = 0, with a=1, b=-3, c=2, the formula gives x = 2 and x = 1.
Frequently asked questions
What is the quadratic formula?
x equals negative b, plus or minus the square root of (b squared minus 4ac), all over 2a. It solves any equation of the form ax squared plus bx plus c equals zero.
What is the discriminant?
The part under the square root, b squared minus 4ac. Positive gives two real roots, zero gives one, and negative gives two complex roots.
What if a is 0?
Then it is a linear equation, not quadratic. The calculator solves bx + c = 0 instead.
Can it give complex roots?
Yes. When the discriminant is negative, it shows the roots in a plus bi form.