NDA 1 2025 Maths, question 49

Solution.

Answer: (d) $\pi/2$

1. The roots are $2 \pm \sqrt{3}$, both positive.
2. For any $k > 0$, the principal angles $\tan^{- 1}k$ and $\tan^{- 1}(1/k)$ are complementary.
3. Therefore their sum is $\pi/2$.
4. Positivity is essential; a negative $k$ would give $- \pi/2$.