Quadratic Equation Calculator
A quadratic equation has x squared as its highest power and is solved with the quadratic formula. Enter a, b and c to see the discriminant and the real roots when they exist.
Your numbers
Result
- Discriminant (Δ)
- 1
- Roots
- Two distinct real roots
| Step | Detail |
|---|---|
| Equation | 1x² + -5x + 6 = 0 |
| Discriminant b² - 4ac | -5² - 4·1·6 = 1 |
| x = (-b ± √Δ) / 2a | x1 = 3, x2 = 2 |
The quadratic formula
For ax² + bx + c = 0, first compute the discriminant Δ = b² - 4ac, then the roots: x = (-b ± √Δ) / 2a. For x² - 5x + 6 = 0: Δ = 25 - 24 = 1, and x = (5 ± 1)/2, giving x1 = 3 and x2 = 2.
What the discriminant tells you
The sign of Δ says how many real roots there are: Δ > 0 gives two distinct roots; Δ = 0 gives one repeated root; Δ < 0 gives no real roots (they are complex). A quick check: the roots add to -b/a and multiply to c/a.
Frequently asked questions
Sources
- Algebra — the quadratic formula
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