8. Fourth-order equation. How many negative roots does the equation

$$
x^{4}-5 x^{3}-4 x^{2}-7 x+4=0 ?
$$

have?
8. The equation $x^{4}-5 x^{3}-4 x^{2}-7 x+4=0$ can be rewritten as $\left(x^{2}-2\right)^{2}=5 x^{3}+7 x$. Since for any negative $x$ the left side of the equation is positive, while the right side is negative, the original equation cannot have negative roots.

[P. E. Horton, M. M., 24, 114 (November 1950).]