Cubic Discriminant Calculator
Actualcubicax³+bx²+cx+d(nonzeroa) polynomialdiscriminantb²c²−4ac³−4b³d−27a²d²+18abcd. Finite binary64, no root certification.
Description
A cubic discriminant depends on its four polynomial coefficients and vanishes at repeated roots in exact arithmetic.
A cubic discriminant depends on its four polynomial coefficients and vanishes at repeated roots in exact arithmetic.1
This tool evaluates the standard coefficient formula using finite floating-point arithmetic.
When to use Cubic Discriminant Calculator
Use this tool to evaluate the standard coefficient formula using finite floating-point arithmetic.
How to use Cubic Discriminant Calculator and how it works
- Prepare a, b, c, d, with the units, conventions and assumptions below.
- Enter the required fields and run Cubic Discriminant Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| a | A. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| b | B. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| c | C. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| d | D. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
Require finite cubic coefficients a,b,c,d with a nonzero. Evaluate b^2*c^2-4*a*c^3-4*b^3*d-27*a^2*d^2+18*a*b*c*d and return the signed discriminant. A zero result can indicate a repeated root, but floating-point cancellation is not a certified root-multiplicity test.
discriminant=b^2*c^2-4*a*c^3-4*b^3*d-27*a^2*d^2+18*a*b*c*d Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Signed cubic discriminant in the supplied coefficient convention. | number |
{
"input": {
"a": 1,
"b": 0,
"c": -1,
"d": 0
},
"output": {
"result": {
"value": 4
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use 2x2 Eigenvectors Calculator for a complementary operation: A real matrix can have real, repeated or complex eigenvalues, and repeated values do not ensure diagonalizability.
Use 2x2 Condition Number Calculator for a complementary operation: A spectral condition number compares the largest and smallest singular values of a matrix.
References
-
Cubic Discriminant Calculator — tool.io
Similar or alternative tools
- 2x2 Eigenvectors Calculator
A real matrix can have real, repeated or complex eigenvalues, and repeated values do not ensure diagonalizability.
- 2x2 Condition Number Calculator
A spectral condition number compares the largest and smallest singular values of a matrix.