Utilizing the Routh-Hurwitz criterion, determine the stability of the following polynomials:
(a) s2 + 5s + 2
(b) s3 + 4s2 + 8s + 4
(c) s3 + 2s2 - 6s + 20
(d) s4 + s3 + 2s2 + 12s + 10
(e) s4 + s3 + 3s2 + 2s + X
(f) s5 + s4 + 2s3 + s + 6
(g) s5 + s4 + 2s3 + s2 + s + K
Determine the number of roots, if any, in the right-hand plane. If it is adjustable, determine the range of K that results in a stable system.