Question

Without solving for the roots, indicate the number of roots in the following polynomial that are in the left half-plane, right half-plane, and on the jo-axis. [Section: 6.2] P(s)s4s⁴ +4s³ +5s² +2s +2

Answer 1

The given polynomial has no real roots in the left half-plane or on the jo-axis, and a total of 4 roots.

Step-by-step explanation:

The given polynomial is P(s) = s^4 + 4s^3 + 5s^2 + 2s + 2.

To determine the number of roots in the left half-plane, right half-plane, and on the jo-axis without solving for the roots, we can look at the coefficients of the polynomial. The coefficients of odd powers of s (s^3, s, s^1) are all positive, so there are no real roots on the jo-axis or in the left half-plane.

Since the polynomial is of degree 4, there will be exactly 4 roots in total.