Quadratic equation solver
Enter a, b and c to get the real or complex roots of the equation. Useful for students and teachers checking homework.
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How to use it
- Enter coefficient a, coefficient b and coefficient c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
x = (-b ± √Δ) / 2a where Δ = b² - 4ac. Δ > 0 gives two real roots, Δ = 0 one repeated root, Δ < 0 two complex conjugate roots. The vertex is at h = -b/2a, k = c - b²/4a.
Example
Inputs: Coefficient a = 1, Coefficient b = -3, Coefficient c = 2. Result: Roots: x1 = 2, x2 = 1; Discriminant Δ: 1; Root type: Two distinct real roots.
Limits and caveats
- Irrational roots are shown as decimals rounded to 10 significant digits, not in surd form.
- a must be non-zero.
Questions about this tool
What is the discriminant?
It is b² - 4ac. A positive value means two real roots, zero means one repeated root, and a negative value means two complex roots.
How do I enter an equation with no x term?
Set b = 0. For 2x² - 8 = 0 enter a = 2, b = 0, c = -8; the roots are 2 and -2.
What does i mean in the result?
i is the imaginary unit, i² = -1. It appears when the discriminant is negative, meaning the parabola never crosses the x axis.