Answer

(i)Given: 2x² + kx + 3 = 0 has equal roots

∴ b² - 4ac = 0

Here a = 2; b = k; c = 3

b² - 4ac

= (k)² - 4()()

k² - = 0

k² =

k = √

k = ±2√

(ii) kx(x-2) + 6 = 0

kx² - 2kx + 6 = 0

As this quadratic equation has equal roots,

b² - 4ac = 0

Here

a = k; b = -2k; c = 6

∴ b² - 4ac

= (-2k)² - 4(k)() = 0

4k² - k = 0

4k(k-) = 0

4k = 0 (or) k - = 0

k = 0 (or)

But k = 0 is trivial

∴ k=.