Question

Find all values of k for which the quadratic equation has no real solutions.4x^2+9x-k=0

Answer 1

`4x^2+9x-k=0`

The discriminant of the quadratic equation is

`b^2-4ac`

whenever this equation becomes a negative number, there are no real solutions to the equation, leading to the following inequality

`b^2-4ac<0`

since a is 4, b is 9, and c is -k.

`\begin{gathered} (9)^2-4\cdot(4)\cdot(-k)<0 \\ 81+16k<0 \\ 16k<-81 \\ k<-(81)/(16) \end{gathered}`

for all values below -81/16 there will be no real solutions.