Quartic Discriminant Calculator
Actual quartic a x⁴+b x³+c x²+d x+e(a≠0), Sylvester resultant(f, f′)/aleadingcoefficient(sign positive for degree4). Finite binary64determinant, no arbitrary precision or root safety.
Description
A polynomial discriminant vanishes at repeated roots and depends on a specified coefficient convention.
A polynomial discriminant vanishes at repeated roots and depends on a specified coefficient convention.1
This tool calculates a quartic discriminant through a Sylvester resultant using finite floating-point arithmetic.
When to use Quartic Discriminant Calculator
This tool calculates a quartic discriminant through a Sylvester resultant using finite floating-point arithmetic.
How to use Quartic Discriminant Calculator and how it works
- Prepare descending quartic coefficients, using the input definitions and matching units below.
- Enter the required fields and run Quartic Discriminant Calculator.
- Read result.quarticDiscriminant using the units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualDescendingQuarticCoefficients | Exactly [a,b,c,d,e] for a*x^4+b*x^3+c*x^2+d*x+e, with a nonzero. | array of number | Required; other constraints below |
Require exactly five finite descending quartic coefficients with nonzero leading coefficient a. Construct derivative coefficients, build the 7-by-7 Sylvester matrix for the quartic and cubic derivative, calculate its determinant and divide by a. Return a binary64 discriminant; the degree-four sign factor is positive. Cancellation and floating-point errors are not certified away.
discriminant=Res(f,fPrime)/leadingCoefficient 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.quarticDiscriminant | Finite quartic discriminant under the stated branch and truncation; no additional numerical certificate. | number |
{
"input": {
"actualDescendingQuarticCoefficients": [
1,
0,
0,
0,
-1
]
},
"output": {
"result": {
"quarticDiscriminant": -256
}
}
}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 Resultant of Two Quadratics Calculator for a complementary operation: The resultant of two quadratics is the determinant of their degree-specific Sylvester matrix.
Use 2x2 Minor Calculator for a complementary operation: A matrix minor is the determinant remaining after deleting a selected row and column.
References
-
Quartic Discriminant Calculator — tool.io
Similar or alternative tools
- Resultant of Two Quadratics Calculator
The resultant of two quadratics is the determinant of their degree-specific Sylvester matrix.
- 2x2 Minor Calculator
A matrix minor is the determinant remaining after deleting a selected row and column.