If $f(x)$ is twice differentiable function such that $f(a)=0 , f(b)=2, f(c)=-1, f(d)=2, f(e)=0,$ where $a<b<c<d<e$ ,then the minimum no. of zero's of $g(x)={f'(x)}^2+f''(x).f(x)$ in the interval $[a,e]$ is ?

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