1. We are given the quadratic equation $$2x^2 + 5x + 4k = 0$$ and told that its discriminant is zero. 2. Recall the discriminant formula: $$\Delta = b^2 - 4ac$$ where $a=2$, $b=5$, and $c=4k$. 3. Substitute $a$, $b$, and $c$ into the discriminant formula: $$\Delta = 5^2 - 4 \cdot 2 \cdot 4k = 25 - 32k$$ 4. Since the discriminant is zero, set $$\Delta = 0$$ and solve for $k$: $$25 - 32k = 0$$ 5. Rearranging: $$32k = 25$$ $$k = \frac{25}{32}$$ 6. Therefore, the value of $k$ that makes the discriminant zero is $$k = \frac{25}{32}$$. Answer: (d) $\frac{25}{32}$.