Enter the coefficients a, b and c of a quadratic equation (ax² + bx + c = 0) to find its roots. Everything runs in your browser — nothing you enter here is uploaded, stored, or logged.
Calculated locally in your browser — nothing is sent to our server.
How This Calculation Works
This calculator uses the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a, to find the value(s) of x that make the equation true. The discriminant (b² − 4ac) determines the nature of the roots: a positive discriminant gives two distinct real roots, zero gives one repeated real root, and a negative discriminant means there is no real solution — in that case, the two roots are complex numbers, shown in the form p ± qi, rather than the calculator showing an error or an incorrect result.
FAQ
What if “a” is zero?
The equation would no longer be quadratic (it would be linear), so the calculator asks for a non-zero value of a.
What does a negative discriminant mean?
It means the equation has no real-number solution — the parabola described by the equation never crosses the x-axis. The two solutions are complex numbers instead.