(i) Since, x = 2 is a root of the given equation, therefore, it satisfies the equation i.e.,
k(2)^{2} + 2 × 2 -3 = 0
⇒ 4k + 1 = 0 ⇒ k = - ¼
(ii) Since, x = -1/2 is a root of the given equation
3x^{2} + 2kx – 3 = 0
Therefore,
3(-1/2)^{2} + 2k(-1/2) - 3 = 0
⇒ 3 × ¼ - k – 3 = 0
⇒ k = ¾ - 3 = - 9/4
⇒ k = - 9/4
(iii) Since, x = - a is a root of the equation
x^{2} + 2ax – k = 0
⇒ (- a)^{2} + 2a × (- a) – k = 0
⇒ a^{2} – 2a^{2} – k = 0
⇒ - k = a^{2} ⇒ k = - a^{2}