Descartes Rule Of Signs
Apply Descartes rule of signs to find the maximum number of positive and negative real roots of a polynomial. Free online algebra tool for students.
About This Calculator
Descartes' rule of signs is a powerful technique for determining the maximum number of positive and negative real roots of a polynomial without solving it. Enter the comma-separated coefficients of your polynomial (from highest degree to constant term) and the calculator counts the sign changes to give you the possible number of real roots.
Frequently Asked Questions
What is Descartes' rule of signs?
Descartes' rule of signs determines the maximum number of positive and negative real roots of a polynomial by counting sign changes in its coefficient sequence.
How do you apply Descartes' rule of signs?
Write the polynomial in standard form with descending powers. Count the number of sign changes between consecutive non-zero coefficients. For negative roots, substitute x with -x and count sign changes again.
What is an example of Descartes' rule?
For polynomial x^3 - 3x^2 + 2x - 1, coefficients are [1, -3, 2, -1]. There are 3 sign changes, so there are 3 or 1 positive real roots.
What are the limitations of Descartes' rule?
Descartes' rule gives the maximum possible number of positive and negative real roots, not the actual count. The actual number can be less by an even number.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration required.