Math
Quadratic Equation Solver
Solve ax² + bx + c = 0. Get the discriminant, real or complex roots, factored form, and vertex.
x²+x+= 0
Discriminant
Δ = 16.0000
Vertex
(0.0000, -4.0000)
Root 1
2.000000
Root 2
-2.000000
Factored Form
(x - 2.0000)(x + 2.0000)
Frequently asked questions
What is the discriminant?
The discriminant (Δ = b² − 4ac) tells you how many real roots exist. Δ > 0 means two distinct real roots. Δ = 0 means one repeated real root. Δ < 0 means two complex (non-real) roots.
What does the vertex represent?
The vertex is the highest or lowest point on a parabola. For a > 0, it's the minimum; for a < 0, it's the maximum. The x-coordinate is -b/(2a).
What if a = 0?
If a = 0, the equation becomes linear (bx + c = 0), not quadratic. Our calculator will show 'Not a quadratic' in that case.
What are complex roots?
When the discriminant is negative, the square root of a negative number produces imaginary numbers. The roots are complex conjugates: one with +i and one with -i.
Solve quadratic equations of the form ax² + bx + c = 0. Enter the coefficients and get the discriminant, roots (real or complex), factored form, and vertex coordinates.