If x satisfies the inequality t a n - 1 x 2 + 3 t a n - 1 x - 4 0 , then the complete set of values of x is

Question

If x satisfies the inequality t a n - 1 x 2 + 3 t a n - 1 x - 4 > 0 , then the complete set of values of x is, - tan ⁡ 4 , π 4, - ∞ , tan ⁡ 4 ∪ π 4 , ∞, tan ⁡ 1 , ∞, tan ⁡ 4 , tan ⁡ 1

MARKS App · Accepted Answer

Let, t a n - 1 x = t the given inequality becomes t 2 + 3 t - 4 > 0 ⇒ t + 4 t - 1 > 0 ∴ t - 4 or t > 1 t a n - 1 x - 4 (not possible) or t a n - 1 x > 1 ⇒ x > tan ⁡ 1

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