Option (C) $\dfrac{3}{2}$
For $p(x) = kx^2 - 30x + 45k$: $\alpha+\beta = \dfrac{30}{k}$ and $\alpha\beta = \dfrac{45k}{k} = 45$.
Given $\alpha+\beta = \alpha\beta$: $\dfrac{30}{k} = 45 \Rightarrow k = \dfrac{30}{45} = \dfrac{2}{3}$.
Wait — Option (D) $\dfrac{2}{3}$.
Source: Chapter 2, Section 2.3
Using the standard result $\alpha+\beta = \frac{-b}{a} = \frac{30}{k}$ and $\alpha\beta = \frac{c}{a} = \frac{45k}{k} = 45$. Setting them equal: $\frac{30}{k} = 45 \Rightarrow k = \frac{2}{3}$. The correct answer is (D). Watch out: the product simplifies to 45 regardless of $k$ (since $\frac{45k}{k}$), so only the sum depends on $k$.