Who is credited with the discovery that the number of possible positive real roots of a polynomial is determined by the number of sign changes in its coefficients?

The discovery that the number of possible positive real roots of a polynomial can be determined by the number of sign changes in its coefficients is attributed to Rene Descartes. This principle is known as Descartes' Rule of Signs. It provides a systematic way to estimate the number of positive roots of a polynomial by examining the sequence of its coefficients. Each time there is a change in the sign from one coefficient to the next, it indicates the potential for a positive root.

For example, if the coefficients of a polynomial are (3, -2, 5, -1), there are three sign changes (from (3) to (-2), from (-2) to (5), and from (5) to (-1)), indicating that there could be up to three positive real roots or possibly one fewer if some roots are double roots. This rule is a crucial tool in algebra for solving polynomial equations and understanding their behavior.

The other individuals listed made significant contributions to mathematics in their own rights, but they are not associated with this specific rule concerning the behavior of polynomial roots.