(i) $s^3+4s^2+5s+2$

$even\ part\ of\ F\left(s\right)=M\left(s\right)=4s^4+2 $

$odd\ part\ of\ F\left(s\right)=N\left(s\right)=s^3+5s $

$Q\left(s\right)=\dfrac{N\left(s\right)}{M\left(s\right)}$

As all terms of equations are positive, the given function is Hurwitz

(ii) $s^4+s^3+2s^2+3s+2$

$Even\ part\ of\ F\left(s\right)=M\left(s\right)=s^4+2s^2+2 $

$Odd\ part\ of\ F\left(s\right)=N\left(s\right)=s^3+3s $

$2\left(s\right)=\dfrac{M\left(s\right)}{N\left(s\right)} $

Since two quotient terms are negative the given function is not Hurwitz