### Instruction: Suppose that $2x^2 - 5x + k = 0$ is a quadratic equation with one solution for $x$. Express $k$ as a common fraction.### Response: To find $k$, I need to use the fact that a quadratic equation has one solution if and only if its discriminant is zero.
The discriminant is the part under the square root in the quadratic formula, which is $b^2 - 4ac$.
In this case, $a = 2$, $b = -5$, and $c = k$, so the discriminant is $(-5)^2 - 4(2)(k) = 25 - 8k$.