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 \[A\cap B=(-2,1)\] \[A/B=(-7,-2)\].You need to login to perform this action.
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