kx (x−2)+6=0⇒ kx 2−2kx +6=0Comparing quadratic equationkx 2−2kx +6=0 with general form ax 2 +bx +c =0, we get a =k , b =−2k and c =6Discriminant = b 2−4ac =(−2k ) 2 – 4(k )(6)=4k 2−24kWe know that two roots of quadratic equation are equal only if discriminant is equal to zero.Putting discriminant equal to zero4k 2−24k =0⇒ 4k (k−6) ⇒ k =0, 6The basic definition of quadratic equation says that quadratic equation is the equation of the form ax 2 +bx +c =0, where a≠0Therefore, in equation kx 2−2kx +6=0, we cannot have k =0.Therefore, we discard k=0.Hence the answer is k=6.