Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula. Enter the values requested below, check the field labels, and use the result in the context of the question you are trying to answer.
Quadratic Formula Tips
The quadratic formula solves equations in the form ax² + bx + c = 0. Enter the a, b, and c coefficients with the correct signs. The discriminant shows whether the answer has two real roots, one repeated real root, or no real roots.
Quick Guide
- Write the equation in standard form first.
- Keep negative signs with the correct coefficient.
- Do not forget the plus-minus symbol.
- Check the discriminant before interpreting roots.
Result
Calculate quadratic roots using the exact values entered above.
Formula and Method
x = (-b ± √(b² - 4ac)) ÷ 2a.
Check the Answer
Review signs, order, units, rounding, and the worked-example guidance before relying on the result.
How the Quadratic Formula Calculator Works
This calculator focuses on quadratic roots. Enter the values requested by the calculator, check that each input matches the topic, and then use the result as a clear math answer rather than a generic estimate.
The most important rule is to match the input format to the formula. Fractions, decimals, signs, units, coordinate order, and rounding choices can all change the result.
Formula or Method
x = (-b ± √(b² - 4ac)) ÷ 2a
| Input | Why It Matters |
|---|---|
| a coefficient | This value controls the quadratic roots result and should be entered carefully. |
| b coefficient | This value controls the quadratic roots result and should be entered carefully. |
| c coefficient | This value controls the quadratic roots result and should be entered carefully. |
Worked Example
For x² - 5x + 6 = 0, the roots are 2 and 3.
When to Use the Quadratic Formula Calculator
- Use the Quadratic Formula Calculator when solving an algebra or coordinate-geometry problem involving quadratic roots.
- Verify graphing work, equation solutions, coordinate pairs, scale drawings, rates, and proportional relationships.
- Test alternate values to see how the equation or point relationship changes.
- Enter a coefficient, b coefficient, c coefficient in the correct order and preserve all positive and negative signs.
Common Mistakes to Avoid
- Forgetting the ± sign.
- Entering coefficients with the wrong sign.
- Misreading the discriminant.
Quadratic Formula Calculator FAQs
What does the Quadratic Formula Calculator find?
It calculates quadratic roots from the values entered on the page.
What formula or method does the Quadratic Formula Calculator use?
The main relationship is: x = (-b ± √(b² - 4ac)) ÷ 2a.
Which inputs matter most for this calculation?
The calculator uses a coefficient, b coefficient, c coefficient. Enter each value in the requested format and keep related units consistent.
Why might my quadratic formula calculator answer differ from a textbook?
A textbook may keep an exact fraction, use a different rounding rule, assume different units, or format an equivalent answer differently.
How can I check the result?
Estimate the expected size or sign first, then substitute the result back into the original relationship when possible.
Should I round before calculating?
Usually no. Keep extra precision during the calculation and round only the final answer unless the problem gives another instruction.