The (mathrm{G}(s) mathrm{H}(mathrm{s})) product of a feedback system is given by [ mathrm{G}(s) mathrm{H}(mathrm{s})=frac{mathrm{K}}{s(s+1)(s+9)} ] Determine if

Question:

The $\mathrm{G}(s) \mathrm{H}(\mathrm{s})$ product of a feedback system is given by

\[
\mathrm{G}(s) \mathrm{H}(\mathrm{s})=\frac{\mathrm{K}}{s(s+1)(s+9)}
\]

Determine if the points given below, lie on the locus of characteristic roots. If yes, find the corresponding value of $\mathrm{K}$.
(a) $s=-0.5$
(b) $s=-2$
(c) $s=j 3$
(d) $s=-0.5+j 0.5$

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