Description
Return sum of root-pair squares from supplied 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 sum of root-pair squares from supplied sum and product.
When to use this tool
Use Symmetric Root Pair Square Sum when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter sum, product. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read squareSum. Use the output convention below.
Return sum of root-pair squares from supplied sum and product. squareSum = sum²-2*product.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sum | Sum | Required. Finite number. |
| product | Product | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| squareSum | Square Sum | Required. Finite number. |
{
"input": {
"sum": 5,
"product": 6
},
"output": {
"squareSum": 13
}
}Limitations and assumptions
- This is an algebraic identity from supplied invariants; real roots, coefficient consistency and actual polynomial roots are not 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
- Quadratic Root Sum Scale Residual
Return scaled expected quadratic root sum and residual.
- Cubic Vieta Pairwise Root Sum
Return cubic pairwise root-product sum.