6-1. Without using the Routh-Hurwitz criterion, determine if the following systems are asymp- totically stable, marginally stable, or unstable. In each case, the closed-loop system transfer func- tion is given. 1 (s+ 5)(s²+2) 10(s+2) (a) M(s) = (b) M(s)= +35²+58 K 100(s-1) (c) M(s) (d) M(s)- +5s +5 (s + 5)(s² + 2s + 2) (e) M(s) 100 -2s²+3s+10 10(s + 12.5) (1) M(s)= +352 + 50s²+s+ 10% 6-2. 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 jo-axis. (a) +252 + 10s + 450-0 (c) + 25s² + 250s +10=0 (b) +252 + 10s + 50 = 0 (d) 2s+ 10 +5.5s² + 5.5x+10=0 (e) s +2s+8 + 15s + 20s² + 16s+ 160 (1) s +2 + 10s² + 20s + 5 = 0