JEE Math Practice Question

Let f : (a, b) $$\to$$ R be twice differentiable function such that $$f(x) = \int_a^x {g(t)dt} $$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :

1. A.twelve roots in (a, b)
2. B.five roots in (a, b)
3. C.seven roots in (a, b)
4. D.three roots in (a, b)