Descartes' Rule of Signs Calculator
The Descartes' Rule of Signs Calculator counts the sign changes in a polynomial's coefficients to bound the number of positive and negative real roots. Enter the coefficients from highest degree to constant, comma-separated.
Formula
Positive roots ≤ sign changes in f(x); negative roots ≤ sign changes in f(−x)
- The actual number of roots differs from the count of sign changes by an even number.
- Enter coefficients including any zeros for missing terms.
x⁴ − 3x³ + 2x − 1
Inputs
- Coefficients (high → low): 1,-3,0,2,-1
Three sign changes give up to 3 (or 1) positive roots; f(−x) gives 1 negative root.
Frequently asked questions
What does Descartes' rule of signs tell you?
The maximum number of positive and negative real roots of a polynomial, based on sign changes in its coefficients.