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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