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kx^2-2kx+6=0\\\\we\ need\ to\ find\ values\ of\ k\ for\ which\ equation\ has\ real\ solutions\\\\determinant=\Delta=4k^2-24k>0\\\\4k(k-6)>0\\\\There\ are\ two\ possibilities\\\\k<0\ and\ k>=6\\

If  0 < k < 6, then Δ is negative.  hence roots are imaginary.
If k = 0, there is no solution.

check it with some sample values of k.