44. A causal LTI system has zero initial condi...

44. A causal LTI system has zero initial conditions and impulses response h(t). Its input x(t) and output y(t) are related through the linear constant-coefficient differential equation

${d^2y(t)\over dt^2}+a{dy(t)\over dt}+a^2y(t)=x(t)$

Let another signal g(t) be defined as

$g(t)=a^2\int^t_0h(\tau)d\tau+{dh(t)\over dt}+ah(t)$

If G(s) is the Laplace transform of g(t), then the number of poles of G(s) is _______.