Consider an even polynomial p(s) given by

$$p(s) = {s^4} + 5{s^2} + 4 + K$$

where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the imaginary axis is __________.

Which one of the following options correctly describes the locations of the roots of the equation s⁴ + s² + 1 = 0 on the complex plane?

A unity feedback control system is characterized by the open-loop transfer function $$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$$ The value of k for which the system oscillates at 2 rad/s is ________.

The transfer function of a linear time invariant system is given by $$H\left(s\right)\;=\;2s^4\;-\;5s^3\;+\;5s\;-\;2$$. The number of zeros in the right half of the s-plane is __________.