Description
Return cubic root product and sign.
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 cubic root product and sign.
When to use this tool
Use Cubic Vieta Root Product Sign when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter leading, constant. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read product, sign. Use the output convention below.
Return cubic root product and sign. Require leading != 0; product = -constant/leading, sign follows it with canonical zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leading | Leading | Required. Finite number. |
| constant | Constant | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| product | Product | Required. Finite number. |
| sign | Sign | Required. Safe integer. |
{
"input": {
"leading": 2,
"constant": -12
},
"output": {
"product": 6,
"sign": 1
}
}Limitations and assumptions
- This assumes a genuine cubic and includes complex roots/multiplicity; no individual roots or complete polynomial are verified.
- 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
- Cubic Vieta Pairwise Root Sum
Return cubic pairwise root-product sum.
- Vieta Root Product Residual
Return a quadratic root-product residual.