question_answer

Find the smallest integral m satisfying the inequality\[\frac{m-5}{{{m}^{2}}+5m-14}>0\]

A)  \[m=-6\]

B)  \[m=-3\]

C)  \[m=-7\]                      

D)  \[m=5\]

Correct Answer: A

Solution :

(a): \[\frac{m-5}{{{m}^{2}}+5m-14}>0\Rightarrow \frac{(m-5)}{(m-2)(m+7)}>0\] Please see the number line below to understand the regions where the above in equation will become positive. Hence the solution is\[m\in (-7,2)\cup (5,\infty )\]