Explanation

(d)
Let 4 and $\alpha$ be roots of given equation
$\therefore 4\alpha = 12\ \ \ \ \ \Rightarrow \alpha = 3$
And $4 + 3 = - p\ \ \ \ \Rightarrow \ \ \ \ p = - 7$
$\therefore$ Equation $x^{2} + px + q = 0$ will reduce to $x^{2} - 7x + q = 0$
Let this equation have $\beta,\ \beta$ as its roots
$\therefore\ \ 2\beta = 7\ \ \ \Rightarrow \ \ \ \beta = \frac{7}{2}$ and $\beta^{2} = q$
$\Rightarrow \ \ \ \ q = \left( \frac{7}{2} \right)^{2} = \frac{49}{4}$