Question

Given the characteristic equation below, what is the number of roots which will be located to the right of the imaginary axis? \[ s^4 + 5s^3 - s^2 - 17s + 12 = 0 \]

• A. One
• B. Two
• C. Three
• D. Zero

Hint:

The Routh-Hurwitz criterion is a quick method for determining the stability of a system by examining the number of roots with positive real parts.

Answer 1

The Correct Option is B

- To determine the number of roots to the right of the imaginary axis, use the Routh-Hurwitz criterion, which helps count the number of unstable poles by forming a Routh array from the characteristic equation.
- The Routh array indicates that there are two poles with positive real parts. 
Conclusion: The number of roots located to the right of the imaginary axis is two, as given by option (B).