When to use this calculator
Check the discriminant of a quadratic equation to understand its real roots. For a nonzero a, positive means two real roots, zero a repeated root, and negative no real roots.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Quadratic Formula Calculator: Find both real or complex roots of a quadratic equation.
PUTTING IT INTO PRACTICE
Quadratic Discriminant: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Coefficient a | 1 |
| Coefficient b | 5 |
| Coefficient c | 6 |
| Result | 1 |
- Check the input labels and enter the example values above.
- Apply the relationship: Discriminant = b² − 4ac.
- The result is 1 , rounded for display.
How to interpret your result
For a nonzero a, positive means two real roots, zero a repeated root, and negative no real roots.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
How do I use the quadratic discriminant calculator?
Enter coefficient a, coefficient b, coefficient c. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Discriminant = b² − 4ac.
What should I check before using the result?
For a nonzero a, positive means two real roots, zero a repeated root, and negative no real roots.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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