Quadratic Formula Calculator

Enter a, b and c — get both roots, real or complex.

ax² + bx + c = 0
Roots
x = 3, 2
Discriminant (b² − 4ac)
1

A positive discriminant means two real roots, zero means one repeated real root, and negative means two complex (imaginary) roots — the sign alone tells you what kind of answer to expect before solving.

A worked example

For x² − 5x + 6 = 0, the discriminant is 1 (positive), giving two real roots: x = 3 and x = 2.

Frequently asked questions

What does the discriminant tell me before I even solve?

Its sign previews the answer: positive means two distinct real roots, exactly zero means one repeated real root (the parabola just touches the x-axis), and negative means no real roots — only complex ones.

What are complex roots, practically speaking?

They mean the parabola described by the equation never crosses the x-axis at all — the 'solutions' exist in the complex number system but don't correspond to real x-intercepts on a standard graph.