Problem: \$\frac{4s + 2}{s(s-1)(s+2)} \$ Expectation of Root Locus Asymptote. (Control Systems)
The angle the asymptotes make with the real-axes is \$\frac{(2 k+1)\pi}{2} \$. The denominator is the number of finite poles minus the number of finite zeros (\$3-1\$). This turns out as \$\frac{\pi}{2}\$ and \$\frac{3 \pi}{2}\$.

Because of one finite zero, one of the loci ends up at that zero. Only the other two go off to \$\infty\$.