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Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane?

Which one of the following options correctly describes the locations of the roots of the equation s4 + s2 + 1 = 0 on the complex plane? Correct Answer Two RHP roots and two LHP roots

CE: s4 + 0s3 + 1s2 + 0s + 1

Routh array

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We have row zero at s3 row

Solving the auxiliary equation, we get:

s4 + s2 + 1 = 0

By differentiating, we get:

4s3 + 2s = 0

The Routh array is modified as shown above.

Observations:

The row of zero indicates symmetric roots about the origin.

2 sign changes below row of zero indicate 2 poles in the right half of the s-plane.

∴ Two poles are on the right side and 2 poles symmetrically lying on left-half.

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