Consider the following equation where the parameter K is nonnegative. (2s + 5)(2s2 + 14s + 49)

Question:

Consider the following equation where the parameter K is nonnegative.
(2s + 5)(2s2 + 14s + 49) + Ks (2s +1)(2s + 3) = 0
Determine the poles and zeros, and sketch the root locus plot.
Use the plot to set the value of K required to give a dominant time constant of ( = 0.5. Obtain the three roots corresponding to this value of K.