Let \(x=2\) be a root of the equation \(x^2+p x+q=0\) and \(f(x)=\left{\begin{matrix}\frac{1-\cos \left({x}^{2}-4px+{q}^…

Let \(x=2\) be a root of the equation \(x^2+p x+q=0\) and
\(f(x)=\left{\begin{matrix}\frac{1-\cos \left({x}^{2}-4px+{q}^{2}+8q+16\right)}{(x-2p{)}^{4}}, & x\neq 2p \\ 0 & x=2p\end{matrix}\right.\)

Then \(\lim _{x \rightarrow 2 p^{+}}[f(x)]\) where [.] denotes greatest integer function, is

[JEE Main 2023, 29 Jan (Shift 1)]