question_answer

If \[A=\left| x\in IR:{{x}^{2}}+6x-7<0\} \right.\] and \[B=\{x\in IR:{{x}^{2}}+9x+14>0\},\] then which of the following is/ are correct?

1. \[(A\cap B)=(-2,1)\]

2. \[(A\backslash B)=(-7,-2)\]

Select the correct answer using the code given below:

A) 1 only              

B) 2 Only

C) Both 1 and 2    

D) Neither 1 nor 2

Correct Answer: C

Solution :

\[{{x}^{2}}+6x-7<0\] \[\Rightarrow \,\,\,(x+7)\,\,(x-1)<0\] \[\Rightarrow \,\,\,x=(-7,1)\] \[\Rightarrow \,\,\,A=\{-7,-6,-5,-4,-3,-2,-1,0,1\}\] \[\Rightarrow \,\,\,{{x}^{2}}+9x+14>0\] \[\Rightarrow \,\,\,(x+7)(x+2)>0\] \[\Rightarrow \,\,\,x=\left( -\infty ,-7 \right)\cup \left( -2,\infty  \right)\] \[\Rightarrow \,\,\,B=R-\{-7,-6,-5,-4,-3,-2\}\] So  \[A\cap B=(-2,1)\] \[A/B=(-7,-2)\].