MATH CALCULATOR
Descartes’ Rule of Signs Calculator
Determine the number of positive and negative real roots of a polynomial using Descartes’ Rule of Signs.
What is the Descartes’ Rule of Signs Calculator & How does it work?
Descartes’ Rule of Signs is a useful tool in algebra that helps determine the possible number of positive and negative real roots of a polynomial. The rule states that the number of positive real roots of a polynomial is equal to the number of sign changes between consecutive nonzero coefficients, or less than that by a multiple of 2.
To find the number of negative real roots, you substitute -x for x in the polynomial and then count the sign changes in the new polynomial. The number of negative real roots is equal to the number of sign changes or less than that by a multiple of 2.
To find the number of negative real roots, you substitute -x for x in the polynomial and then count the sign changes in the new polynomial. The number of negative real roots is equal to the number of sign changes or less than that by a multiple of 2.
P(x) = a_n x^n + a_{n-1} x^{n-1} + cdots + a_1 x + a_0
a_i = coefficients of the polynomial
Parameters
Result—
Frequently Asked Questions
What is Descartes' Rule of Signs?
Descartes' Rule of Signs helps determine the possible number of positive and negative real roots of a polynomial by counting sign changes in its coefficients.
How do I use this calculator?
Enter your polynomial equation into the calculator, and it will provide you with the possible number of positive and negative real roots based on Descartes' Rule of Signs.
Can this calculator handle polynomials with complex coefficients?
No, this calculator is designed for polynomials with real coefficients only.
What does a sign change mean in the context of Descartes' Rule of Signs?
A sign change occurs when two consecutive nonzero coefficients in the polynomial have opposite signs.
How accurate is this calculator?
The calculator provides an exact result based on Descartes' Rule of Signs, which is a mathematical theorem.
Can I use this calculator for polynomials with repeated roots?
Yes, the calculator can be used for polynomials with repeated roots, but it will only count distinct sign changes.
What if my polynomial has no real roots?
If there are no sign changes in the polynomial or after substituting -x for x, then there are no positive or negative real roots, respectively.
Results are for informational purposes only and do not constitute professional advice.