Help me solve this exercise?

Question

Which are the values of "k" ,k belongs (is included) in R..for wich the innequation x^2 - (k-3)*x - k+6 < 0 has no solutions ?

Answer 1

(k-3)^2+4(k+6)<=0
k^2-2k+33<=0 never so the innequation has always solutions
ask^2-2k+33 = (k-1)^2+32

Answer 2

x^2 - (k-3)*x - k+6 < 0

if k = 5 then the vertex of the parabola is at (1, 0) and you have the equation equaling 0. For any value of k > 5 ,the expression will be less than 0.