Find the value(s) of k so that the quadratic equation 3x² – 2kx + 12 = 0 has equal roots? (CBSE 2012)

We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero.

Discriminant is equal to 0, is given by

b² – 4ac = 0 …(i)

Comparing 3x² – 2kx + 12 = 0 with general quadratic equation ax² + bx + c = 0, we get

a = 3, b = -2k and c = 12

Substituting these values in equation (i), we get

(-2k)² – 4(3)(12) = 0

⇒ 4k² – 144 = 0

⇒ 4k² = 144

⇒ k² = 144/4 = 36

⇒ k = ±6

Hence, the values of k are 6 and -6.