Description
Return scaled expected quadratic root sum and 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 scaled expected quadratic root sum and residual.
When to use this tool
Use Quadratic Root Sum Scale Residual when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter leading, linear, suppliedRootSum, suppliedVariableScale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read expectedScaledSum, residual. Use the output convention below.
Return scaled expected quadratic root sum and residual. Require leading and suppliedVariableScale nonzero; expectedScaledSum = (-linear/leading)*scale, residual = suppliedRootSum-expected.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leading | Leading | Required. Finite number. |
| linear | Linear | Required. Finite number. |
| suppliedRootSum | Supplied Root Sum | Required. Finite number. |
| suppliedVariableScale | Root-coordinate multiplier; expectedScaledSum=(-linear/leading)*suppliedVariableScale. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| expectedScaledSum | Expected Scaled Sum | Required. Finite number. |
| residual | Signed observed/calculated-minus-reference difference under the operation specified above. | Required. Finite number. |
{
"input": {
"leading": 2,
"linear": -6,
"suppliedRootSum": 7,
"suppliedVariableScale": 2
},
"output": {
"expectedScaledSum": 6,
"residual": 1
}
}Limitations and assumptions
- The scale multiplies root coordinates under this convention; no complete variable substitution, individual roots or coefficient validation is performed.
- 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 Separation From Discriminant
Return separation of real quadratic roots from a supplied discriminant.
- Symmetric Root Pair Square Sum
Return sum of root-pair squares from supplied sum and product.