$($ii$)$ Using the Routh$-$Hurwitz criterion, determine the stability of the closed$-$loop system that has the following characteristic equations. Determine the number of roots of each equation that are in the right$-$half s$-$plane and on the $j-$axis.

$($a$)s^3+25s^2+250s+10=0$

$($b$)s^6+2s^5+8s^4+15s^3+20s^2+16s+16=0$