Quadratic Discriminant Calculator
Discriminant and root type for ax²+bx+c.
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
- 1
- Root nature
- Two distinct real roots
- a, b, c
- 1, -3, 2
Quick answer
The discriminant b^2-4ac tells you the nature of the roots: positive gives two real roots, zero gives one repeated root, negative gives complex roots.
D = b^2 - 4ac
At a glance
| What it does | Discriminant and root type for ax²+bx+c. |
|---|---|
| Category | Math |
| Inputs needed | a, b, c |
| Main output | Discriminant |
| Formula | D = b^2 - 4ac |
| Cost | Free — no sign-up, no download |
How to use the Quadratic Discriminant Calculator
- 1Enter the quadratic coefficients a, b and c.
- 2Compute D = b^2 - 4ac.
- 3The sign of D tells you what kind of roots the equation has.
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-3
- c2
Results
- Discriminant1
- Root natureTwo distinct real roots
- a, b, c1, -3, 2
Frequently asked questions
What if D is negative?
The equation has no real solutions; the roots are complex numbers.
What if a = 0?
It's not a quadratic — use the linear equation solution instead.
What do I need to enter into the Quadratic 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 Quadratic Discriminant Calculator work out the answer?
The discriminant b^2-4ac tells you the nature of the roots: positive gives two real roots, zero gives one repeated root, negative gives complex roots. It applies the formula D = b^2 - 4ac and shows the working so you can check each step by hand.
Is the Quadratic 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.