For what values of k does the quadratic equation


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



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

It is given that, it has no real roots.

$\Rightarrow$ Discriminant $<0$

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


$\Rightarrow 144+16 k<0$

$\Rightarrow 16 k<-144$

$\Rightarrow k<-9$

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


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