Make Routh tables and tell how many roots of the following two polynomials are in the right half plane and in the left half plane. P(s) = s5 + 3s4 + 5s3 + 4s2 + s + 3 (1) P(s)=3s7 + 9s6 + 6s5 + 4s4 + 7s3 + 8s2 + 2s + 6

P(s) = s5 + 3s4 + 5s3 + 4s2 + s

For above Polynomial, there are two RHP Poles & Three LHP Poles.

& for the Second Polynomial,

P(s)=3s7 + 9s6 + 6s5 + 4s4 + 7s3 + 8s2 + 2s + 6

For this Polynomial, there are Four RHP Poles & Three LHP Poles.

Explanation:

As the equation is given by for the first polynomial,

P(s)=s5 + 3s4 + 5s3 + 4s2 + s

The Routh table is attached in the attachment, & from that table we can see that there are two sign changes for thuis first ploynomial. Moreover, there are two RHP poles & Three LHP Poles.

Similarly the equation for the second polynomial is given by as,

P(s)=3s7 + 9s6 + 6s5 + 4s4 + 7s3 + 8s2 + 2s + 6

The Routh Table is attached in the same attachment below in the 2nd slide & from this table we can see that there are four sign changes for this polynomial while it includes Four RHP Poles & three LHP Poles.

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explanation: