For a given value of k , the product of the roots of x2−2kx+3k2−4=0  is 5. The roots may be characterized as:

The given equation is x2−2kx+3k2−4=0 Here a=1,b=−2k,c=3k2−4 Given that, product of roots=5 ⇒  3k2−4=5  ⇒  3k2=9  ⇒  k2=3 .Now Discriminant=4k2−4(3k2−4)=16−8k2        (∵Δ=b2−4ac) =16−24=−8<0 ⇒  Roots are imaginary.