CAT 1994 — QA Question 12

If one root of x² + px + 12 = 0 is 4, then 4² + 4p + 12 = 0, i.e. p = –7.

x² – px + q = 0 has equal roots.

If the roots are α each, 2α = - $\frac{(-7)}{1}$ = 7, i.e., α = $\frac{7}{2}$, and q = α²

$\Rightarrow q=\frac{49}{4}$

Hence, option (a).