Quadratic Equation Solver

A quadratic equation has the form ax² + bx + c = 0 with a ≠ 0. The discriminant, b² − 4ac, tells you the nature of the roots before you solve: positive and a perfect square means two rational roots; positive otherwise, two irrational roots (surds); zero, one repeated root; negative, no real roots (two complex roots).

Choose the method your textbook uses. Factorisation works when b² − 4ac is a perfect square; completing the square and the formula always work. Every root is substituted back into the equation with exact arithmetic before it's shown.

Set Roots to "Real roots only" when a question asks only for real solutions; choose "Real and complex" to see complex roots as a ± bi.

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

b² − 4ac

the discriminant

Sum of roots

−b/a

Product of roots

c/a