Question

A system has the following characteristic polynomial equation and it has three sign changes in the first column of Routh array. Choose correct choice for the number of roots on right and left side of s-plane. \[ s^4 + 3s^3 + 10s^2 + 5s + 10 = 0 \]

• A. 3 roots on right side & 2 roots on left side
• B. 2 roots on right side & 3 roots on left side
• C. 4 roots on right side & 1 root on left side
• D. 1 root on right side & 4 roots on left side

Hint:

Number of right-hand plane roots = number of sign changes in the first column of the Routh array.

Answer 1

The Correct Option is A

According to Routh-Hurwitz criterion, the number of sign changes in the first column of the Routh array corresponds to the number of poles in the right-half s-plane. Since there are 3 sign changes, the system has 3 roots on the right side and 2 on the left side.