Descartes’ Rule of Signs
Descartes’ Rule of Signs with explicit inputs, formulas and domain checks.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Counts include multiplicity. These are possibilities, not an exact root solver; complex roots are not individually listed.
Example Calculation
- Polynomial coefficients: 1, -3, 2
x²−3x+2 has two sign changes: either2 or0 positive roots by this rule; its actual roots are1 and2.
Frequently asked questions
How do I use this calculator?
Enter polynomial coefficients. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Positive roots: sign changes in P(x), or fewer by an even number. Negative roots: sign changes in P(−x).. Counts include multiplicity. These are possibilities, not an exact root solver; complex roots are not individually listed.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.