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Quadratic Discriminant Calculator — result sheet
Calculate the discriminant and classify the real-root count of a quadratic equation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Discriminant Δ = b²−4ac; Δ>0 gives two real roots, Δ=0 one repeated real root, and Δ<0 no real roots.
The discriminant is computed before any square root, so the root-count classification remains valid even when the roots are not real.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Coefficient a — minimum -1000000; maximum 1000000
- Coefficient b — minimum -1000000; maximum 1000000
- Coefficient c — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Coefficient a | 1 |
| Coefficient b | -5 |
| Coefficient c | 6 |
Δ = 1; two distinct real roots.
Assumptions and limits
- Coefficient a is nonzero so the equation is genuinely quadratic.
- Coefficients are finite real numbers within the displayed bounds.
- Complex roots are classified but not returned as symbolic complex values.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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