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Question

The greatest negative integer satisfying $x^{2} + 4 x - 77 < 0$ and $x^{2} > 4$ is

- 1

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Solution

The correct option is B $- 3$
$(x - 2) (x + 2) > 0$
$x \in (- \infty, - 2) \cup (2, + \infty)$ --- (1)
$((x + 2)^{2} - 81) < 0$
$(x + 2 - 9) (x + 2 + 9) < 0$
$(x - 7) (x + 11) < 0$
$\Rightarrow x \in (- 11, 7)$ --- (2)
$x \in (- 11, - 2) \cup (2, 7)$
Greatest negative integer $= - 3$ .

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