The question has worded incorrectly.
The author should have worded: Find the values of k for which: ("3k-5)x2 + 2(4-k)x + 4 is"
and not: " . . . (3k-5)x2 +2(4-k)x + 4 = 0 is"
because only the quadratic function, (in this case) can be positive definite etc etc, and not the corresponding quadratic equation.