Determine whether the system is stable, and determine the values of the roots.

P$6\mathrm{.}15$ The stability of a motorcycle and rider is an important area for study $12,13.$ The handling characteristics of a motorcycle must include a model of the rider as well as one of the vehicle. The dynamics of one motorcycle and rider can be represented by the loop transfer function

$L(s)=\frac{K(s^2+30s+1125)}{s(s+20)(s^2+10s+125)(s^2+60s+3400)}$

$($a$)$ As an approximation, calculate the acceptable range of $K$ for a stable unity negative feedback system when the numerator polynomial $($zeros$)$ and the denominator polynomial $(s^2+60s+3400)$ are neglected. $($b$)$ Calculate the actual

range of acceptable $K,$ account for all zeros and poles.