Decartes Rule of Signs
Rene Descartes came up with a rule of signs that can be used to find the number of possible positive and negative solutions to a polynomial equation.
Positive Roots
The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or less than it by a multiple of 2. Multiple roots of the same value are counted separately.
Negative Roots
As a corollary of the rule, the number of negative roots is the number of sign changes after negating the coefficients of odd-power terms (otherwise seen as substituting the negation of the variable for the variable itself), or fewer than it by a multiple of 2. {Wikipedia}
To use type in an expression of any 6th degree or less polynomial into the input box, f(x). To clear click on the Reset Button or if the yellow fields do not work click on the reset button.