Calculating your discriminant (b² − 4ac) is straightforward once you know the Discriminant formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Discriminant Calculator.
What is Discriminant?
The Discriminant calculation tells you your discriminant (b² − 4ac) from a few simple inputs. The figure you are solving for here is the discriminant (b² − 4ac).
The Discriminant formula
The core formula is:
Discriminant (b² − 4ac) = b ^ 2 - 4 × a × cHere is what each input means:
- a — a number. Example: 1.
- b — a number. Example: 5.
- c — a number. Example: 6.
How to calculate it step by step
- Write down the a (for example, 1).
- Write down the b (for example, 5).
- Write down the c (for example, 6).
- Apply the formula above to get your discriminant (b² − 4ac).
- Double-check the result with the Discriminant Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| a | 1 |
| b | 5 |
| c | 6 |
| Discriminant (b² − 4ac) | 1.0000 |
With a of 1, b of 5 and c of 6, the discriminant (b² − 4ac) works out to 1.0000.
Example 2
With a of 2, b of 5 and c of 6, the discriminant (b² − 4ac) works out to -23.0000.
| Result | Value |
|---|---|
| Discriminant (b² − 4ac) | -23.0000 |
Example 3
With a of 5, b of 5 and c of 6, the discriminant (b² − 4ac) works out to -95.0000.
| Result | Value |
|---|---|
| Discriminant (b² − 4ac) | -95.0000 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Discriminant Calculator does it instantly, for free, with the formula and a worked example built in.
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