What does a zero discriminant mean?
It means both quadratic-formula branches produce the same repeated real root.
Quadratic Formula Calculator
Solve real or complex roots of ax² + bx + c = 0.
Calculations happen locally. We do not send your values to our server.
Example
For x² − 5x + 6 = 0, entering a=1, b=−5, and c=6 returns the roots 2 and 3.
Calculation method
The discriminant is b²−4ac. Real roots use (−b ± √discriminant)/(2a); a negative discriminant produces a complex conjugate pair.
Important notes
The coefficient a cannot be zero because that would make the equation linear rather than quadratic.
Frequently asked questions
Can this show complex roots?
Yes. A negative discriminant is returned as a real part plus or minus an imaginary part.
Does it factor the polynomial?
No. It calculates the roots directly from the coefficients.