An algebra problem by Saikat Sengupta

Let $p$ and $q$ be 2 integers. And the 2 roots of the equation (in $x$ ) below

$x^2 - \dfrac{p^2+11}9 x + \dfrac{15}4 (p+q) + 16 = 0$

is also $p$ and $q$ . Which of the following pairs of can represent the values of $p$ and $q$ ?