Description
Return a quadratic root-product residual.
Polynomial coefficients encode powers in a chosen order, with zeros, multiplicities and leading terms carrying different meanings. Local coefficient identities and necessary divisibility conditions can be checked without finding every root or proving a proposed factorization. Floating-point comparisons use the exact supplied values unless an explicit tolerance is provided.
Return a quadratic root-product residual.
When to use this tool
Use Vieta Root Product Residual when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter a, c, firstRoot, secondRoot. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Return a quadratic root-product residual. Require a != 0; residual = firstRoot*secondRoot-c/a.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Finite number. |
| c | C | Required. Finite number. |
| firstRoot | First Root | Required. Finite number. |
| secondRoot | Second Root | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Signed observed/calculated-minus-reference difference under the operation specified above. | Required. Finite number. |
{
"input": {
"a": 2,
"c": 12,
"firstRoot": 2,
"secondRoot": 4
},
"output": {
"residual": 2
}
}Limitations and assumptions
- A zero residual checks only one Vieta relation, not that supplied values are roots of a complete quadratic.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete symbolic or numerically appropriate polynomial method for root finding, full factorization and robust treatment of near-degenerate coefficients.
References
Similar or alternative tools
- Algebra: Quadratic Vieta Coefficient Pair
Return quadratic Vieta sum and product.
- Polynomial Double Root Coefficient Constraint
Check exact quadratic double-root discriminant.