Complex Numbers And Quadratic Equations question 646
Question: If $ A=| x\in IR:x^{2}+6x-7<0} . $ and $ B={x\in IR:x^{2}+9x+14>0}, $ then which of the following is/ are correct?
- $ (A\cap B)=(-2,1) $
- $ (A\backslash B)=(-7,-2) $ Select the correct answer using the code given below:
Options:
A) 1 only
B) 2 Only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
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=( -\infty ,-7 )\cup ( -2,\infty ) $
$ \Rightarrow B=R-{-7,-6,-5,-4,-3,-2} $ So $ A\cap B=(-2,1) $ $ A/B=(-7,-2) $ .
BETA
