Our Descartes’ Rule of Signs calculator helps you determine the possible number of positive and negative real roots for any polynomial equation.

Enter the coefficients of the polynomial separated by commas (e.g., 1, -3, 2, -4 for x^3 – 3x^2 + 2x – 4):

## How it works:

Descartes’ Rule of Signs is a technique for estimating the number of positive and negative real roots of a polynomial. It states that the number of positive real roots of a polynomial is either equal to the number of sign changes between its consecutive nonzero coefficients or less than that by an even number. Similarly, the number of negative real roots can be determined by applying the rule to the polynomial with its signs altered in a pattern (+, −, +, −, …).

## How to use this calculator:

Enter the coefficients of your polynomial into the input field, separated by commas. For instance, if you have a polynomial x^3 – 3x^2 + 2x – 4, you would input “1,-3,2,-4”. Then click the “Calculate” button to get the estimated number of positive and negative real roots.

## Limitations:

This calculator provides an estimate, not an exact count. It does not tell you the exact number of real roots but rather the maximum possible number, which could be less by an even number. This calculator also does not account for complex roots and assumes all the inputted coefficients are real numbers. Only the sign changes are counted, so zeroes between the coefficients should not be entered.

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