Mark the Correct alternative in the following:
If x is real and , then
(x2 + x + 1)k = (x2 – x + 1)
(k – 1)x2 + (k + 1)x + (k – 1) = 0
For roots of quadratic equation real
Case I : a ≠ 0 and D ≥ 0
k – 1 ≠ 0 ⇒ k ≠ 1
-3k2 + 10k – 3 ≥ 0
3k2 – 10k + 3 ≤ 0
or
or
Case II : a = 0
k – 1 = 0 ⇒ k = 1
At k = 1, 2x = 0 ⇒ x = 0 is real
So, k = 1 is also count in answer.
Then, final answer is k ∈ [1/3, 3]