question_answer

The smallest integer x for which the in equality  \[\frac{x-5}{{{x}^{2}}+5x-14}\,\,>0\] is satisfied is given: by -

A) \[-\,6\]

B) \[-\,5\]   

C) \[-\,4~\]

D) \[-\,8\]

Correct Answer: A

Solution :

\[\frac{(x-5)}{{{x}^{2}}+5x-14}>0\]\[\frac{(x-5)}{(x+7)(x-2)}>0\]

\[x\in (-\,7,2)\cup (5,\infty )\]

Smallest integer x is \[-\,6\]