The trick here is to find the discriminant, b^2-4ac, of the equation 2x^2 - 5x + k.
Here a=2, b=-5, and c=k.
So long as the discriminant is 0 or greater than 0, your roots will be real and rational numbers.
Thus, compute b^2-4ac: (-5)^2 - 4(2)(k)
Let this equal zero and solve for k: 25=8k; k=25/8.
So long as k is 25/8 or smaller, b^2-4ac will be 0 or greater, and the roots will be real and rational.
