Description
Return quadratic Vieta sum and product.
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 quadratic Vieta sum and product.
When to use this tool
Use Algebra: Quadratic Vieta Coefficient Pair when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter a, b, c. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return quadratic Vieta sum and product. Require a != 0; rootSum = -b/a, rootProduct = c/a.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Finite number. |
| b | B | Required. Finite number. |
| c | C | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the returned operation-specific members listed below. | Required. Object. |
| result.rootSum | Root Sum | Calculated result member: number. |
| result.rootProduct | Root Product | Calculated result member: number. |
{
"input": {
"a": 2,
"b": -6,
"c": 4
},
"output": {
"result": {
"rootSum": 3,
"rootProduct": 2
}
}
}Limitations and assumptions
- The identities include complex roots and multiplicity; no discriminant, individual root values or real-root guarantee is supplied.
- Outputs are nested inside result. 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
- Quadratic Root Sum Scale Residual
Return scaled expected quadratic root sum and residual.
- Quadratic Root Separation From Discriminant
Return separation of real quadratic roots from a supplied discriminant.