Discriminant Calculator
b² − 4ac tells you how many roots a quadratic has.
Enter your values
Enter the a you are working with.
Enter the b you are working with.
Enter the c you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Discriminant Δ
- 1
- Nature of roots
- Two distinct real roots
- Roots
- 2 and 3
- Perfect square?
- Yes — the quadratic factors over the rationals
- Vertex x
- 2.5
Quick answer
The discriminant b² − 4ac decides the roots: positive means two real roots, zero means one repeated root, negative means two complex roots.
Δ = b² − 4ac
At a glance
| What it does | b² − 4ac tells you how many roots a quadratic has. |
|---|---|
| Category | Math |
| Inputs needed | a, b, c |
| Main output | Discriminant Δ |
| Formula | Δ = b² − 4ac |
| Cost | Free — no sign-up, no download |
How to use the Discriminant Calculator
- 1Enter the coefficients a, b and c.
- 2Read the discriminant's sign to see the root count.
- 3Check whether it is a perfect square to know if the quadratic factors neatly.
Inputs explained
- a
- Enter the a you are working with.
- b
- Enter the b you are working with.
- c
- Enter the c you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- a1
- b-5
- c6
Results
- Discriminant Δ1
- Nature of rootsTwo distinct real roots
- Roots2 and 3
- Perfect square?Yes — the quadratic factors over the rationals
- Vertex x2.5
Frequently asked questions
What does a discriminant of zero mean graphically?
The parabola just touches the x-axis at its vertex — a double root.
Does the discriminant work for cubics?
There is a cubic discriminant, but the b² − 4ac form applies only to quadratics.
What do I need to enter into the Discriminant Calculator?
Just 3 values: a, b, c. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Discriminant Calculator work out the answer?
The discriminant b² − 4ac decides the roots: positive means two real roots, zero means one repeated root, negative means two complex roots. It applies the formula Δ = b² − 4ac and shows the working so you can check each step by hand.
Is the Discriminant Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.