The characteristic equation of a system is [ s^{3}+10 s^{2}+(50+mathrm{A}) s+mathrm{K}=0 ] Determine the regions on A-K

Question:

The characteristic equation of a system is

\[
s^{3}+10 s^{2}+(50+\mathrm{A}) s+\mathrm{K}=0
\]

Determine the regions on A-K plane (A on $\mathrm{X}$ axis and $\mathrm{K}$ on $\mathrm{Y}$ axis) in which the closed-loop system is asymptotically stable and unstable. Indicate boundary on which the system is marginally stable.

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