Given the unity feedback system of Figure P$8\mathrm{.}3,$ make an accurate plot of the root locus for the following:

a$.G(s)=\frac{K(s^2-2s+2)}{(s+1)(s+2)}$

b$.G(s)=\frac{K(s-1)(s-2)}{(s+1)(s+2)}$

Also, do the following:

Calibrate the gain for at least four points for each case. Also find the breakaway points, the $j-$axis crossing, and the range of gain for stability for each case. Find the angles of arrival for Part a$.[$Section: $8\mathrm{.}5]$

Solve b