Rigula
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Locale-aware

Quadratic equation solverUS · en-US

Enter three coefficients and inspect roots, discriminant, vertex, and symmetry axis.

ax² + bx + c = 0

Ready.

How to use it

Use this solver for a genuine quadratic polynomial with finite numeric coefficients.

  1. Enter coefficients a, b, and c, with a not equal to zero.
  2. Solve the equation and identify whether the discriminant is positive, zero, or negative.
  3. Review both roots and the parabola's vertex and symmetry axis.

Worked example

Input
x² − 5x + 6 = 0
Output
Roots 3 and 2 · discriminant 1 · vertex (2.5, −0.25)

A negative discriminant produces a conjugate pair written with i.

Method and definitions

  • The discriminant is b²−4ac and the vertex is (−b/2a, −discriminant/4a).
  • Real roots use a stable q formulation where possible to reduce cancellation; complex roots use the quadratic formula.

Limits and edge cases

  • a = 0 is a linear equation and is intentionally rejected.
  • Results use finite binary floating point and do not provide symbolic fractions or arbitrary precision.

Privacy

All input and output stays in this tab. Rigula does not upload, store, or include it in a share URL.