How to use this calculator
Enter the coefficients a, b and c of a*x^2 + b*x + c = 0. Use a nonzero a for a quadratic equation. Review the discriminant and roots, then compare the plotted range with the root locations.
Method and interpretation
The discriminant is b^2 - 4ac. A positive value gives two distinct real roots, zero gives a repeated real root, and a negative value gives a complex conjugate pair. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a).
Assumptions and limits
A graph is a sampled illustration and may not show every important feature if its range is too narrow. Coefficients and plot bounds must be finite, and the sampling range must be bounded. Rounded roots may leave a small residual when substituted back into the equation.
Worked example
For x^2 - 5x + 6 = 0, a = 1, b = -5 and c = 6. The discriminant is 25 - 24 = 1. The roots are (5 + 1)/2 = 3 and (5 - 1)/2 = 2.