Set, Relation and FunctionMedium
Question
The range of k for which the inequality k cos2x - k cos x + 1 ≥ 0 ∀ x ∈ R, is -
Options
A.k < 
B.k > 4
C. ≤ k ≤ 4
≤ k ≤ 4D. ≤ k ≤ 2
≤ k ≤ 2Solution
We have k cos2x - k cosx + 1 ≥ 0
⇒ k(cos2x - cos x) + 1 ≥ 0
cos2x - cos x = (cos x -
)2 - 
Since - ≤ cos2x - cos x ≤ 2
We have 2k + 1 ≥ 0 and -
+ 1 ≥ 0
⇒ -
≤ k ≤ 4
⇒ k(cos2x - cos x) + 1 ≥ 0
cos2x - cos x = (cos x -
)2 - Since -
≤ cos2x - cos x ≤ 2 We have 2k + 1 ≥ 0 and -
+ 1 ≥ 0⇒ -
≤ k ≤ 4Create a free account to view solution
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