If the roots of the quadratic equation (4p - p² - 5)x² - (2p - 1)x + 3p = 0 lie on either side of unity, then the number of integral values of p is

Note that coefficient of x² is (4p - p² - 5) < 0. Therefore, the graph is concave downward. According to the question, 1 must lie between the roots. Hence,

$\begin{array}{l}\mathrm{f}\left(1\right)>0\\ \Rightarrow 4\mathrm{p}-{\mathrm{p}}^2-5-2\mathrm{p}+1+3\mathrm{p}>0\\ \Rightarrow -{\mathrm{p}}^2+5\mathrm{p}-4>0\\ \Rightarrow {\mathrm{p}}^2-5\mathrm{p}+4<0\\ \Rightarrow (\mathrm{p}-4)(\mathrm{p}-1)<0\\ \Rightarrow 1<\mathrm{p}<4\\ \Rightarrow \mathrm{p}\in \{2,3\}\end{array}$