The characteristic equation of an LTI system is given by
F(s) = s⁵ + 2s⁴ +3s³ + 6s² - 4s - 8 = 0.The number of roots that lie strictly in the left half s-plane is _____.

Consider a transfer function $$G_p\left(s\right)\;=\;\frac{ps^2+3ps\;-2}{s^2+\left(3+p\right)s\;+\left(2-p\right)}$$ with 'p' a positive real parameter. The maximum value of 'p' until which G_p remains stable is ________.

The feedback system shown below oscillates at 2 rad/s when

The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$