# Number of roots?

Calculus Level 4

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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