Sorry! The question is:
The equation 2x^2-3x-(k+1)=0 where k is a constant, has no real roots. Find the set of possible values of k.
Therefore the discriminant must be <0 for f(x) to have no real roots. Therefore discriminant=(-3)^2-4(-k-1)(2)=17+8k
Therefore 17+8k<0
Therefore 8k<-17
Therefore k<-17/8