Final answer:
The value of k for the quadratic equation 2x^2 - 5x + k = 0 to have one solution is 25/8.
Step-by-step explanation:
If a quadratic equation has exactly one solution for x, it means that the discriminant (the part of the quadratic formula under the square root) is equal to zero. For a quadratic equation in the form ax^2 + bx + c = 0, the discriminant is b^2 - 4ac. When the equation 2x^2 - 5x + k = 0 has one solution, the discriminant (-5)^2 - 4(2)(k) must be zero.
Calculating this gives us 25 - 8k = 0. Therefore, 8k = 25, and when we solve for k, we get k = 25/8. So, the value of k when the equation has one solution for x is 25/8, which is the common fraction representation of k.