Descartes' rule of signs

Descartes' Rule of Signs helps estimate the number of positive and negative real roots (solutions) of a polynomial equation. For positive roots, it counts how many times the signs of the coefficients change in the polynomial; the number of positive roots is either equal to that or less than it by an even number. To find negative roots, substitute \(-x\) for \(x\) and count sign changes in the resulting polynomial. This rule provides an upper bound and possible count of real roots, helping to narrow down solutions before further analysis.