Ex.1

Solve[s + 2 == 0, s]

Solve[s^2 + s + 2 == 0, s]

Solve[s^3 + s^2 + s + 2 == 0, s]

NSolve[s^3 + s^2 + s + 2 == 0, s]

Solve[s^5 + s^4 + s^3 + s^2 + s + 2 == 0, s]

NSolve[s^5 + s^4 + s^3 + s^2 + s + 2 == 0, s]

FindRoot[s^5 + s^4 + s^3 + s^2 + s + 2 == 0, {s, 0}]

FindRoot[s^5 + s^4 + s^3 + s^2 + s + 2 == 0, {s, I}]

Ex.2

ans = 
      NSolve[s^3 + s^2 + s - 1 == 0, s]
Re[s  /.  ans]

Ex.3

a = 1
b = 1
y = 
        InverseLaplaceTransform[1/(s^2 + a*s + b)*1/s, s, 
          t];
Solve[s^2 + a*s + b == 0, s]
g1 = Plot[y, {t, 0, 15}]
Clear[a, b]