Question 914680
g(x) and f(x) intersect at one point --> f(x) - g(x) = 2x^2 - 5x + 3 - 3x - k = 2x^2 - 8x + (3-k) has exactly one real solution.


The discriminant is 64 - 4(2)(3-k), setting to zero (so that the quadratic has one solution) gives us (4)(2)(3-k) = 64 --> k = -5.