A unity feedback system has the loop transfer function:

$G_c(s)G(s)=\frac{K}{s(s+2)(s+5)}$

Find $($a$)$ the breakaway point on the real axis and the gain K for this point; $($b$)$ the grain and the roots when two roots lie on the imaginary axis, and $($c$)$ the roots when $K=6.($d$)$ Sketch the root locus by hand. Verify your root locus using MATLAB function "rlocus".