An algebra problem by Saikat Sengupta

Algebra Level 4

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 \(q\)?

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