Description
Check exact quadratic double-root discriminant.
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.
Check exact quadratic double-root discriminant.
When to use this tool
Use Polynomial Double Root Coefficient Constraint 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 residual, doubleRoot. Inspect doubleRoot before interpreting the associated values.
Check exact quadratic double-root discriminant. Require a != 0; residual = b²-4*a*c, doubleRoot tests residual === 0.1
| 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 |
|---|---|---|
| residual | Signed observed/calculated-minus-reference difference under the operation specified above. | Required. Finite number. |
| doubleRoot | Exact zero discriminant test; no tolerance or robust near-root classification. | Required. Boolean. |
{
"input": {
"a": 2,
"b": -8,
"c": 8
},
"output": {
"residual": 0,
"doubleRoot": true
}
}Limitations and assumptions
- No tolerance or stable discriminant algorithm is added; floating-point equality does not establish a numerically reliable near-double-root classification.
- 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 Completing Square Offset
Return completing-square shift and vertical offset.
- Quadratic Discriminant Roundoff Scale
Return a magnitude scale for discriminant arithmetic.