The integer k , for which the inequality x 2 - 2 3 k - 1 x + 8 k 2 - 7 0 is valid for every x in R is:

Question

The integer k , for which the inequality x 2 - 2 3 k - 1 x + 8 k 2 - 7 > 0 is valid for every x in R is:, 4, 2, 3, 0

MARKS App · Accepted Answer

x 2 - 2 3 k - 1 x + 8 k 2 - 7 > 0 Now, D 0 ⇒ 4 3 k - 1 2 - 4 × 1 × 8 k 2 - 7 0 ⇒ 9 k 2 - 6 k + 1 - 8 k 2 + 7 0 ⇒ k 2 - 6 k + 8 0 ⇒ k - 4 k - 2 0 ⇒ k ∈ 2 , 4 ⇒ k = 3

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