Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system that has the following characteristic equations.

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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

(a) \(s^{3}+25 s^{2}+10 s+450=0\)

(b) \(s^{3}+25 s^{2}+10 s+50=0\)

(c) \(s^{3}+25 s^{2}+250 s+10=0\)

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