About quadratic equation solver
A quadratic equation has the form ax² + bx + c = 0. The solver gives its roots and the discriminant.
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The part under the root, b² − 4ac, is the discriminant.
What the discriminant tells you
- Positive: two different real roots.
- Zero: one repeated real root.
- Negative: no real roots, only complex ones.
Example
x² − 5x + 6 = 0 has discriminant 25 − 24 = 1, so x = (5 ± 1) ÷ 2, giving 3 and 2.
Another worked example
For 2x² − 7x + 3 = 0, the discriminant is 49 − 24 = 25, so x = (7 ± 5) ÷ 4, giving 3 and 0.5. For x² + 2x + 5 = 0 the discriminant is −16, so there are no real roots, only complex ones, −1 ± 2i.
Checking your answer
- Add the roots: it should equal −b ÷ a.
- Multiply them: it should equal c ÷ a.
