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"Check the following polynomials for Hurwitz \[ \left(1 \right) P\left(s \right)=s^5+4s^4+3s^3+s^2+4s+1 \\ \left(2 \right) P\left(s \right)=s^4+4s^2+8 \]"
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(1) $p(s)= s^5 + 4s^4+3s^3 +s^2+4s +1$

 Routh array is given by

$\left.\begin{array}{ cccccc} s^5 \\ s^4 \\ s^3 \\ s^2 \\ s \\ s^0 \end{array}\right\vert{}\begin{array}{ cccccc} 1 & 3 & 4 \\ 4 & 1 & 1 \\ 2.75 & 3.75 & \\ -4.45 & 1 & \\ 4.367 …

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