Math
Quadratic Solver
Solve ax² + bx + c = 0 in seconds, including discriminant analysis and whether roots are real or complex.
algebrarootsquadratic
Quadratic Solver
Solve ax² + bx + c = 0 with discriminant analysis.
Discriminant
1
Root 1
2
Root 2
1
Nature
Two real roots
Quadratic formula
x = [−b ± √(b² − 4ac)] ÷ (2a)
The discriminant Δ = b² − 4ac reveals the nature of roots: Δ > 0 gives two real roots, Δ = 0 gives a repeated real root, and Δ < 0 yields complex conjugates.
How to use
- Enter coefficients a, b, and c for your quadratic equation.
- Ensure a ≠ 0; otherwise the equation is linear and cannot use the quadratic formula.
- Read the discriminant, roots, and root nature in the results panel.
Example
Input: a = 1, b = -3, c = 2
Output: Discriminant = 1, Roots = 2 and 1 (two real roots)
FAQ & notes
What happens if a = 0?
The calculator treats the expression as invalid because the quadratic formula requires a non-zero a coefficient. Adjust your equation or switch to a linear solver.
How are complex roots displayed?
When the discriminant is negative, roots are shown as a conjugate pair in the form real ± imaginary·i.