Find the value(s) of k so that the quadratic equation has equal roots.

Question

Find the value(s) of k so that the quadratic equation  has equal roots.

Philoid · Accepted Answer

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.