Question

find the value of k for which the equation kx(x-2)+6=0!!!1hw help

Answer 1

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

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.