How to use this calculator
Find the real roots of ax² + bx + c = 0. Enter coefficient a, coefficient b, coefficient c. The result updates when you change an input. To compare two sets of inputs, save scenario A, then enter the second set; the result panel shows the difference.
Formula and limits
Roots = [−b ± √(b² − 4ac)] ÷ 2a. For numerical stability, one root is calculated without subtracting nearly equal values and the other from the product of the roots. Requires a ≠ 0 and a nonnegative discriminant. Complex roots are not shown.
Worked example
The following example uses the calculator’s starting values. It is an illustration of the method, not a recommended target.
| Input | Example value |
|---|---|
| Coefficient a | 1 |
| Coefficient b | -5 |
| Coefficient c | 6 |
First real root: 3
Second root: 2
Interpreting your result
Use consistent units when a calculator asks for lengths or areas. Negative inputs are accepted only where the operation supports them. Display rounding does not change the underlying formula.
Comparing alternatives
Save the first result as scenario A, then change one input. The comparison shows the numeric difference; it does not label either result as better. Choose inputs that describe realistic alternatives. Values shown on screen are rounded, so calculations from rounded intermediate results may differ slightly.
Background reading
OpenStax Algebra and Trigonometry. This is a subject reference, not an endorsement or independent review of Calcaven.