For a given value of$k$ , the product of the roots of $x^2-2kx+3k^2-4=0$  is 5. The roots may be characterized as:

The given equation is $x^2-2kx+3k^2-4=0$

Here $a=1,b=-2k,c=3k^2-4$

Given that, product of roots$=5$

$\Rightarrow$  $3k^2-4=5$

 $\Rightarrow$  $3k^2=9$  $\Rightarrow$  $k^2=3$ .

Now Discriminant$=4k^2-4\left(3k^2-4\right)=16-8k^2$        $\left(\because \Delta =b^2-4ac\right)$

$=16-24=-8<0$

$\Rightarrow$  Roots are imaginary.