Resultant of Two Quadratics Calculator
Degree-two Sylvester resultant actual descending coefficients, sign conventionRes(f, g), not discriminant or fully solve common roots.
Description
The resultant of two quadratics is the determinant of their degree-specific Sylvester matrix.
The resultant of two quadratics is the determinant of their degree-specific Sylvester matrix.1
This tool calculates that scalar from descending coefficients without solving for common roots.
When to use Resultant of Two Quadratics Calculator
This tool calculates that scalar from descending coefficients without solving for common roots.
How to use Resultant of Two Quadratics Calculator and how it works
- Prepare first quadratic descending coefficients, second quadratic descending coefficients, using the input definitions and matching units below.
- Enter the required fields and run Resultant of Two Quadratics Calculator.
- Read result.quadraticResultant 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 |
|---|---|---|---|
| actualFirstQuadraticDescendingCoefficients | Exactly [a,b,c] for a*x^2+b*x+c, with a nonzero. | array of number | Required; other constraints below |
| actualSecondQuadraticDescendingCoefficients | Exactly [d,e,f] for d*x^2+e*x+f, with d nonzero. | array of number | Required; other constraints below |
Require two arrays of exactly three descending quadratic coefficients, with each leading coefficient nonzero. Construct the 4-by-4 Sylvester matrix with two shifted rows of each polynomial and return its determinant in the Res(first,second) convention. Finite binary64 arithmetic can incur cancellation; zero is not an independent exact common-root certificate.
resultant=det([[a,b,c,0],[0,a,b,c],[d,e,f,0],[0,d,e,f]]) 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.quadraticResultant | Finite degree-two Sylvester resultant under the stated branch and truncation; no additional numerical certificate. | number |
{
"input": {
"actualFirstQuadraticDescendingCoefficients": [
1,
0,
-1
],
"actualSecondQuadraticDescendingCoefficients": [
1,
0,
-4
]
},
"output": {
"result": {
"quadraticResultant": 9
}
}
}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 Quartic Discriminant Calculator for a complementary operation: A polynomial discriminant vanishes at repeated roots and depends on a specified coefficient convention.
Use 2x2 Minor Calculator for a complementary operation: A matrix minor is the determinant remaining after deleting a selected row and column.
References
-
Resultant of Two Quadratics Calculator — tool.io
Similar or alternative tools
- Quartic Discriminant Calculator
A polynomial discriminant vanishes at repeated roots and depends on a specified coefficient convention.
- 2x2 Minor Calculator
A matrix minor is the determinant remaining after deleting a selected row and column.