Number of roots?

Calculus Level 5

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

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