Question

The number of roots of $s^3+5s^2+7s+3=0$ in the left half of the s-plane is

• A. zero
• B. one
• C. two
• D. three

Answer 1

The correct option is D three

Using R-H criterion:
$\begin{array}{ccc}{s}^3& 1& 7\\ s^2& 5& 3\\ s^1& 6.4& 0\\ s^0& 3& \end{array}$
There is no sign change in the first column if R-H array. So, there is no roots lie in R.H.S of s-plane. So, all the 3 roots will lie in the left half of s-plane.