(i) kx^{2 }+ 2x + 3k = 0
Here, a = k, b = 2, and c = 3k
Sum of roots = - b/a = - 2/k
Product of roots = c/a
= 3k/k = 3
Sum of roots = Product of roots
-2/k = 3
⇒ 3k = - 2
⇒ k = - 2/3
(ii) 2x^{2} – (3k + 1)x – k + 7 = 0
Here, a = 2,
b = -(3k + 1)
c = - k + 7
Sum of roots = - b/a
= 3k + ½
Product of roots = c/a
= - k + 7/2
Sum of roots = Product of roots
3k + 1/2 = - k + 7/2
6k + 2 = - 2k + 14
8k = 12, ⇒ k = 12/8
∴ k = 3/2