The discriminant of the quadratic equation is
[tex]b^2-4ac[/tex]whenever this equation becomes a negative number, there are no real solutions to the equation, leading to the following inequality
[tex]b^2-4ac<0[/tex]since a is 4, b is 9, and c is -k.
[tex]\begin{gathered} (9)^2-4\cdot(4)\cdot(-k)<0 \\ 81+16k<0 \\ 16k<-81 \\ k<-\frac{81}{16} \end{gathered}[/tex]for all values below -81/16 there will be no real solutions.
