GATE Electrical Engineering (EE) 2018 Solved Paper

Characteristic equation,

${\mathit{S}}^7$	1	7	31	25
${\mathit{S}}^6$	1	14	73	200
${\mathit{S}}^5$	$-7$	$-42$	$-175$	0
${\mathit{S}}^4$	8	48	200	0
${\mathit{S}}^3$	32	96	0	0
${\mathit{S}}^2$	24	200	0	0
${\mathit{S}}^1$	$-170$	0	0	0
${\mathit{S}}^0$	200	0	0	0

Auxiliary equation, $\mathit{A}\left(\mathit{s}\right)=8{\mathit{s}}^4+48{\mathit{s}}^2+200$
$\frac{\mathit{d}}{\mathit{d}\mathit{s}}\mathit{A}\left(\mathit{s}\right)=32{\mathit{s}}^3+96\mathit{s}$
Total no of poles $=7$
Two sign change above auxiliary equation $=2$ poles in RHS
Two sign changes below auxiliary equation implies out of 4 symmetric roots about. origin two poles are in LHS and two poles are in RHS.
$\therefore 3$ poles in LHS and 4 poles in RHS.