Math
Quadratic Formula Calculator
Solve ax² + bx + c = 0 using the quadratic formula.
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 Quadratic Formula 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 to the section you need, then return to the quadratic formula 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.
Quadratic Formula Calculator formula guide
Use these quadratic formula calculator formulas to audit the output or explain it to someone else.
2 formulas
Quadratic Formula Calculator examples
Review a ready-made quadratic formula calculator 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
Learn more
Guides connected to the quadratic formula calculator
Use these short guides when you want the decision framework behind the numbers, not just the raw output.
Category guide
Math Calculator Guide
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Directly related
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FAQ
Quadratic Formula Calculator FAQ
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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