For equal roots, discriminant = 0: $b^2 - 4ac = 0$.
Here $a = 9$, $b = 8k$, $c = 16$.
$(8k)^2 - 4(9)(16) = 0 \Rightarrow 64k^2 = 576 \Rightarrow k^2 = 9 \Rightarrow k = \pm 3$
Answer: A (3) and B (−3) — both are valid, but the options listed include A: 3 and B: −3.
Source: Chapter 4, Section 4.4
For equal roots, use $b^2 - 4ac = 0$. Here $b = 8k$, so $(8k)^2 = 64k^2$. Solving gives $k = ±3$. Both A and B are correct values; if only one option must be chosen, note that the question likely expects both but most MCQs here accept either. Examiners award mark for correct application of discriminant condition.