Description
Return a magnitude scale for discriminant arithmetic.
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 a magnitude scale for discriminant arithmetic.
When to use this tool
Use Quadratic Discriminant Roundoff Scale 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 scale. Use the output convention below.
Return a magnitude scale for discriminant arithmetic. scale = abs(b²)+abs(4*a*c).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 |
|---|---|---|
| scale | abs(b)^2+abs(4*a*c); a magnitude reference, not a certified roundoff bound or tolerance. | Required. Finite number. |
{
"input": {
"a": 2,
"b": 3,
"c": -4
},
"output": {
"scale": 41
}
}Limitations and assumptions
- This is a cancellation/reference scale, not a rigorous roundoff bound, tolerance or proof of discriminant sign; a may be zero.
- 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.
- Polynomial Double Root Coefficient Constraint
Check exact quadratic double-root discriminant.