Description
Return separation of real quadratic roots from a supplied 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.
Return separation of real quadratic roots from a supplied discriminant.
When to use this tool
Use Quadratic Root Separation From Discriminant when checking the stated coefficient, root-identity, index or divisibility term.
How to use the tool and how it works
- Enter discriminant, leading. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read separation. Use the output convention below.
Return separation of real quadratic roots from a supplied discriminant. Require discriminant >= 0 and leading != 0; separation = sqrt(discriminant)/abs(leading).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| discriminant | Discriminant | Required. Finite number. |
| leading | Leading | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| separation | sqrt(discriminant)/abs(leading), the nonnegative real-root separation for nonnegative discriminant. | Required. Finite number. |
{
"input": {
"discriminant": 9,
"leading": 2
},
"output": {
"separation": 1.5
}
}Limitations and assumptions
- The discriminant is not derived or verified; this returns absolute separation, not actual roots or numerical conditioning.
- 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.
- Quartic Root Product From Coefficients
Return quartic root product from two coefficients.