Using the Routh$-$Hurwitz Criterion method, determine whether the system with the following

closed$-$loop transfer function is stable or unstable?

The answer contains manual calculations $($hand calculations$)$ and calculation validation using Octave

software $($screenshot of the results of running the Octave program$)$

a$.G(s)=\frac{1000s}{6s^2-7s-24}$

b$.G(s)=\frac{10}{2s^3+3s^2+12s+14}$

c$.G(s)=\frac{1}{s^3+2s^2+6}$