For a twice differentiable function f(x), g(x) is defined as g(x)=(f'(x))^{2} + f(x)f''(x). For constants a < b < c < d < e, we have
f(a)=0, f(b)=2, f(c)=-1, f(d)=2, f(e)=0.

Find the minimum number of roots of the equation g(x)=0 in the interval (a, e).