For what values of x the expression $x^{2} - 5 x - 14$ is positive ?

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Solution

$x^{2} - 5 x - 14 > 0$
$x^{2} - 7 x + 2 x - 14 > 0$
$(x - 7) (x + 2) > 0$
$\Rightarrow x < - 2$ or $x > 7$
Hence for $x \in (- \infty, - 2) \cup (2, \infty)$ , the expression $x^{2} - 5 x - 14$ is positive.

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