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Quadratic Equation Calculator — result sheet
Solve ax^2 + bx + c = 0 for its real roots and inspect the discriminant.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: D = b^2 - 4ac; x = (-b +/- sqrt(D)) / (2a).
A positive discriminant gives two real roots, zero gives a repeated root, and a negative discriminant gives no real roots. Power-of-two coefficient scaling protects tiny inputs, and a cancellation-resistant quadratic formula preserves the smaller root when coefficient magnitudes differ substantially. The first result is the smaller root.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Coefficient a — Must be nonzero.; minimum -1000000000000; maximum 1000000000000
- Coefficient b — minimum -1000000000000; maximum 1000000000000
- Coefficient c — minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Coefficient a | 1 |
| Coefficient b | -3 |
| Coefficient c | 2 |
1; 2
Assumptions and limits
- Only real roots are reported; negative discriminants are rejected with an explanation.
- Coefficient a must be nonzero; use a linear solver for a = 0.
- Results use floating-point arithmetic. Excessively wide coefficient ratios are rejected, and nearly repeated roots have precision limits.
- A nonzero discriminant too small to represent numerically is shown in scaled notation rather than incorrectly displayed as zero.
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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