8. For the cubic function $y=x^{3}+a x^{2}+b x+c$, its graph intersects the $x$-axis at points $A, T$, and $B$ in sequence. The lines $A P$ and $B Q$ are tangent to the cubic curve at points $P$ and $Q$ (where $P$ does not coincide with $A$, and $Q$ does not coincide with $B$). Then the ratio of the projections of $\overrightarrow{A B}$ and $\overrightarrow{P Q}$ on the $x$-axis is:
8. -2

Let the coordinates of $A, B, P$ be $(\alpha, 0), (\beta, 0), \left(x_{1}, y_{1}\right)$, and let $T(\gamma, 0)$, then
$$
y=(x-a)(x-\beta)(x-\gamma)
$$

For the line $y=m(x-\beta)$ passing through $A$ and intersecting (1) at two points, the x-coordinates of these two points are given by $(x-\beta)(x-\gamma)-m$. When these two points coincide, then $m=-(\beta-\gamma)^{2} / 4, x_{1}=(\beta+\gamma) / 2$, which means the projection of $P$ on the x-axis $\left(x_{1}, 0\right)$ is the midpoint of $B T$. Similarly, the projection of $Q$ on the x-axis is also the midpoint of $A T$. Therefore, the ratio of the projections of $\overrightarrow{A B}$ and $\overrightarrow{P Q}$ on the x-axis is -2 (since the projections of $\overrightarrow{A B}$ and $\overrightarrow{P Q}$ on the x-axis are in opposite directions).