Let \(f:(a, b) \rightarrow R\) be twice differentiable such that \(f(x)=\int_a^x g(t) d t\) for a differentiable functio…

Let \(f:(a, b) \rightarrow R\) be twice differentiable such that \(f(x)=\int_a^x g(t) d t\) for a differentiable function \(g(x)\). If \(f(x)=0\) has exactly five distinct roots in \((a, b)\), then \(g(x) g^{\prime}(x)=0\) has at least:

[JEE Main 2021, 27 Jul (Shift 2)]