📐 Descartes Rule of Signs Calculator
Count sign changes to estimate roots
How to Use This Calculator
Enter the coefficients of your polynomial in descending order (from highest degree to constant).
For example, for x³ - 6x² + 11x - 6, enter: 1,-6,11,-6
Descartes Rule of Signs
For Positive Roots: Count the number of sign changes in the polynomial f(x).
For Negative Roots: Count sign changes in f(-x).
The number of positive (or negative) roots is either equal to the number of sign changes or is less than it by an even number.
Example: x³ - 6x² + 11x - 6
Sign pattern: +, -, +, - → 3 sign changes
Therefore, there are 3 or 1 positive roots
About Descartes Rule of Signs Calculator
Descartes' Rule of Signs estimates the number of positive and negative roots of a polynomial by counting sign changes. It provides an upper bound, not an exact count.
Frequently Asked Questions
What does this rule tell us?
Number of sign changes gives upper bound on positive roots.
Can the number of roots be less than sign changes?
Yes, by an even number. For example, 3 sign changes means 3 or 1 positive roots.