Descartes' Rule of Signs

Counts the possible positive and negative real zeros from a polynomial's sign changes.

Descartes' Rule of Signs: the number of positive real zeros of $f$ equals the number of sign changes in $f(x)$ 's coefficients, or less by an even number. The number of negative real zeros equals the number of sign changes in $f(-x)$ 's coefficients, or less by an even number.

Examples

$f(x) = 2x^4 - x^3 - 3x^2 + x - 1$ has 3 sign changes, so 3 or 1 positive real zeros.