It is important to point out that the condition for the breakaway point given in Eq.
(F-20) is necessary but not sufficient. In other words, all breakaway points on the root
loci for all values of K must satisfy Eq. (F-20), but not all solutions of Eq. (F-20) are
breakaway points. To be a breakaway point, the solution of Eq. (F-20) must also satisfy
the equation 1 KG1(s)H1(s) 0, that is, must also be a point on the root loci for some
real K. In general, the following conclusions may be made with regard to the solutions
of Eq. (F-20):