polynomial roots

Consider the polynomial p(s) = s^5 + 7s^4 + 3s^3 - 33s^2 + 2s - 40. Let (L, I, R) be defined as follows. L is the number of roots of p(s) with negative real parts. I is the number...

Consider p(s) = s 3 + $${a_2}$$s 2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(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 ____...

A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has