Quadratic Formula
Solve quadratic equations and find roots
How to use Quadratic Formula
- 1Enter the coefficients a, b, and c from your quadratic equation a x^2 + b x + c = 0.
- 2Make sure a is not zero, otherwise the equation is linear, not quadratic.
- 3Read the roots, the discriminant, and whether the solutions are real or complex.
Solving quadratics
x = (-b ± √(b² - 4ac)) / (2a); discriminant D = b² - 4acThe quadratic formula finds the two values of x where the parabola crosses the axis; the discriminant tells you how many real solutions exist.
If the discriminant is positive there are two real roots, zero gives one repeated root, and negative gives two complex conjugate roots.
Frequently asked questions
What does the discriminant tell me?
Its sign reveals the nature of the roots: positive for two real, zero for one, negative for two complex.
Why are there two answers?
A squared term generally yields two symmetric solutions; the plus and minus in the formula captures both.
What if a is zero?
Then it is a linear equation with one solution; enter it into a linear solver instead.