Q. 115.0( 1 Vote )

# Mark the Correct alternative in the following:If x is real and , thenA. k ∈ [1/3,3]B. k ≥ 3C. k ≤ 1/3D. none of these

(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]

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