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Descartes Rule of Signs Calculator
Count possible positive and negative real roots of a cubic using Descartes rule of signs.
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Possible positive real roots
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Count possible positive and negative real roots of a cubic using Descartes rule of signs.
Descartes Rule of Signs Estimator
Enter your numbers below for an instant estimate.
0
💡 Tip: Count sign changes in f(x) and f(-x).
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
Descartes Quick Guide
Typical values for reference.
| x3 | x2 | x | Positive roots |
|---|---|---|---|
| 1 | -6 | 11 | 3 or 1 positive |
| 1 | 0 | 0 | 1 positive |
| 1 | 2 | 3 | 0 positive |
| 1 | -1 | -1 | 2 or 0 positive |
| Rule of Thumb | Check inputs | Use as a guide | Round sensibly |
Common Questions
Descartes Rule of Calculator FAQ
Answers to common questions about this calculator.
It bounds the number of positive and negative real roots.
Count sign changes in f(-x).
It gives possible counts, not exact roots.
Zero coefficients are skipped.