Question

For what values of k does the quadratic equation 4x² –12x – k = 0 have no real roots?

Answer 1

Let 4x² –12x – k = 0 be a quadratic equation.

It is given that, it has no real roots.

$$\begin{gathered} \Rightarrow \mathrm{Discriminant}<0 \\ \Rightarrow b^2-4ac<0 \\ \Rightarrow {\left(-12\right)}^2-4\left(4\right)\left(-k\right)<0 \\ \Rightarrow 144+16k<0 \\ \Rightarrow 16k<-144 \\ \Rightarrow k<-9 \end{gathered}$$

Hence, the values of k must be less than –9.