Inputs
Adjust the assumptions to match your scenario. Results update instantly.
Results
Primary outputs and comparison insights are built from the current inputs.
Discriminant
1
b² − 4ac determines the nature of roots.
Root 1
3
First solution of the equation.
Root 2
2
Second solution of the equation.
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How this calculator works
The Quadratic Formula Calculator solves any second-degree polynomial equation ax² + bx + c = 0 and shows the discriminant. Enter a (x² coefficient), b (x coefficient), and c (constant) to estimate discriminant, root 1, and root 2. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision.
Quick guide
Jump straight to the section you need, then return to the calculator.
Inputs
- Coefficient of x².
- Coefficient of x.
- Constant term.
Outputs
- b² − 4ac determines the nature of roots.
- First solution of the equation.
- Second solution of the equation.
Assumptions
- Coefficient a must be non-zero.
- Only real roots are computed.
Tips
- Positive discriminant = 2 real roots, zero = 1, negative = complex.
- Factor first when possible for cleaner answers.
Formula guide
Use these formulas to audit the output or explain it to someone else.
2 formulas
Usage examples
Review a ready-made scenario, copy it, then tweak inputs to match your case.
Example
Standard equation
Inputs
- Example input a (x² coefficient): 2
- Example input b (x coefficient): -7
- Example input c (constant): 3
Outputs
- Example result Discriminant: 25
- Example result Root 1: 3
- Example result Root 2: 0.5
2x²−7x+3=0 factors to (2x−1)(x−3)=0, giving x=0.5 and x=3.
Roots by constant c
| c (constant) | Discriminant | Root 1 |
|---|---|---|
| 2 | 17 | 4.56 |
| 4 | 9 | 4 |
| 6 | 1 | 3 |
| 8 | -7 | 0 |
| 10 | -15 | 0 |
When the discriminant is negative, there are no real roots.
Discriminant sensitivity
Focus point
2
17
Position
#1 of 5
Original order
Change vs previous
—
Select another point to compare
When the discriminant is negative, there are no real roots.
References
- Quadratic formula derivation
- Discriminant analysis in algebra
FAQ
Common questions
What does the Quadratic Formula Calculator do?
The Quadratic Formula Calculator solves any second-degree polynomial equation ax² + bx + c = 0 and shows the discriminant. Enter a (x² coefficient), b (x coefficient), and c (constant) to estimate discriminant, root 1, and root 2. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision. It is part of our math toolkit.
What inputs do I need?
Typical inputs include Coefficient of x²., Coefficient of x., Constant term..
How are the results calculated?
We follow the formulas and assumptions outlined in the "How this calculator works" section. You will see outputs like b² − 4ac determines the nature of roots., First solution of the equation., Second solution of the equation..
Can I share or download the results?
Use the Copy link or Print buttons to share your results. If a table or chart appears, you can download the data as CSV.
Is my data stored?
No. Calculations run in your browser and we do not store your inputs.
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