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Complex Root Calculator
Find the real or complex roots of a quadratic equation.
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Roots
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Find the real or complex roots of a quadratic equation.
Complex Root Estimator
Enter your numbers below for an instant estimate.
0
💡 Tip: x = (-b +/- sqrt(b2 – 4ac)) / 2a.
How It Works
Key concepts behind this calculator
1
Enter Values
Fill in each field with your own numbers.
2
Calculate
Results update as you change the inputs.
3
Review
Read the breakdown and the explanation.
4
Adjust
Change values to compare scenarios.
Quick Reference Guide
Complex Quick Guide
Typical values for reference.
| a | b | c | Roots |
|---|---|---|---|
| 1 | 2 | 5 | -1.000 +/- 2.000i |
| 1 | 0 | 4 | 0.000 +/- 2.000i |
| 1 | -3 | 2 | 2.000 and 1.000 |
| 2 | 4 | 5 | -1.000 +/- 1.225i |
| Rule of Thumb | Check inputs | Use as a guide | Round sensibly |
Common Questions
Complex Root Calculator FAQ
Answers to common questions about this calculator.
A root with a nonzero imaginary part, found when the discriminant is negative.
Yes, as conjugates, for real coefficients.
b2 – 4ac, it decides the type of roots.
Substitute a root back into the equation.