The number of roots in the left half of the s-plane of the given equation s^3 + 3s^2 + 4s + 1 = 0 is: - Automatic Control Systems

Electronics and Communication Engineering (ECE) : Automatic Control Systems - Quiz(MCQ)

The number of roots in the left half of the s-plane of the given equation s^3 + 3s^2 + 4s + 1 = 0 is:

A)

One

B)

Two

C)

Three

D)

Zero

Correct Answer : Option (C) : Three

Explanation : The given characteristic equation is: s^3 + 3s^2 + 4s + 1 = 0.

To find the number of roots, we need to create a Routh table, as shown below:

There are no roots and no significant changes in the RHS plane, as shown in the above table. Hence, all three roots lie in the LHS plane.

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