# For what values of k does the quadratic equation

Question:

For what values of $k$ does the quadratic equation $4 x^{2}-12 x-k=0$ have no real roots?

Solution:

Let $4 x^{2}-12 x-k=0$ be a quadratic equation.

It is given that, it has no real roots.

$\Rightarrow$ Discriminant $<0$

$\Rightarrow b^{2}-4 a c<0$

$\Rightarrow(-12)^{2}-4(4)(-k)<0$

$\Rightarrow 144+16 k<0$

$\Rightarrow 16 k<-144$

$\Rightarrow k<-9$

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