Limits Continuity And Differentiability

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

Then \(\mathop {\lim }\limits_{x \to 2{p^ + }} [f(x)]\), where \(\left[ . \right]\) denotes greatest integer function, is