# JEE Main 2016 (20)

Calculus Level 5

For a twice diffrentiable 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 $$(a,e)$$.

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