$S^8+5S^6+2S^4+3S^2+1$=0. Examine the stability of the system by using earth’s alteration.$S^8+5S^6+2S^4+3S^2+1$=0

All the elements of $S^7$ row in array are zero The auxillary equation of $S^8$ row is, A(S)=$S^8+5S^6+2S^4+3S^2+1$ $\frac{dA(S)}{ds}$=$8S^7+30S^5+8S^3+6S$

Comment: System is unstable since there are two sign changes in the first column.