For what value of k, are the roots of the quadratic equation kx (x – 2) + 6 = 0 equals? (CBSE 2013)

The given Quadratic Equation is-

kx(x – 2) + 6 = 0

i.e. kx²-2kx+6 = 0

For Equal Roots, D should be equal to zero.

Discriminant D of the quadratic equation ax²+bx+c = 0 is given by-

D = b²-4ac

Comparing the equation ax²+bx+c = 0 with given quadratic equation kx²-2kx+6 = 0, we get-

a = k, b = –2k and, c = 6

∴ D = 0

⇒ (-2k)²-24k = 0

⇒ 4k²-24k = 0

⇒ 4k(k-6) = 0

⇒ k=0 or (k-6)=0

∴ k=0 or k=6

but k=0 is invalid, because then the given quadratic equation will become linear.

Hence, the required value of k is 6.