(i) The given equation is :
kx^{2} – 6x – 2 = 0
Here, a = k, b = - 6 & c = - 2
This equation has real root if
b^{2} – 4ac ≥ 0
⇒ (- 6)^{2} – 4 × k × (- 2) ≥ 0
⇒ 36 + 8k ≥ 0
⇒ 8k ≥ - 36
⇒ k ≥ - 36/8 ⇒ k ≥ - 9/2
(ii) The given quadratic equation is :
9x^{2} + 3kx + 4 = 0
Here, a = 9, b = 3k and c = 4
This equation has real roots if
b^{2} – 4ac ≥ 0
⇒ (3k)^{2} – 4 × 9 × 4 ≥ 0
⇒ 9k^{2} – 144 ≥ 0
⇒ 9k^{2 } ≥ 144
⇒ k^{2 } ≥ 144/9 ⇒ k ≥ 12/3
⇒ k ≥ 4.