According to Descartes' rule of signs, the equation x⁴ + 5x³ - x² + 7x + 9 = 0 has -

In $f(x) = x^4 + 5x^3 - x^2 + 7x + 9$, the sequence of coefficient signs $(+, +, -, +, +)$ has two sign changes, so by Descartes' rule of signs the equation has at most two positive roots. Similarly, $f(-x) = x^4 - 5x^3 - x^2 - 7x + 9$ has two sign changes, giving at most two negative roots.