Chapter 5.9, Problem 12P

In each of Problems $12$ through $15$, use the Routh criterion to find the range of $K$ for which all the poles of the transfer functions are in the left half of the complex plane. Then use a computer program to verify your answers by plotting the poles in the s-plane for various values of $K$.

$\frac{K\left(s+1\right)}{s^3+5s^2+\left(K-6\right)s+K}$