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Quadratic Roots Calculator — result sheet
Solve a quadratic equation and show its discriminant and real or complex roots.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For ax² + bx + c = 0, D = b² − 4ac and x = (−b ± √D)/(2a).
The discriminant identifies whether the quadratic has two real roots, one repeated real root, or a conjugate complex pair.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Coefficient a — The leading coefficient cannot be zero.; 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 |
D = 1; roots are x₁ = 3 and x₂ = 2.
Assumptions and limits
- a, b, and c are finite real coefficients and a is not zero.
- Complex results are displayed in rectangular form when the discriminant is negative.
- No symbolic simplification beyond the numerical roots is attempted.
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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