Question

If $A=[x\epsilon R;x^2+6x-7<0]$ and $B=[x\epsilon R:x^2+9x+14>0]$, then which of the following is/are correct?
1. $A\cap B=[x\epsilon R:-2<x<1]$

2. $A\cup B=[x\epsilon R:-7<x<-2]$

Select the correct answer from the given alternatives.

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is A 1 only

For set $A$, $x^2+6x-7<0⟹(x+7)(x-1)<0⟹x\in (-7,1)$

For set $B$, $x^2+9x+14>0⟹(x+2)(x+7)>0⟹x\in (-\infty ,-7)\cup (-2,\infty )$

$\therefore A\cap B⟹(-2,1)$.

$\therefore A\cup B⟹(-\infty ,-7)\cup (-7,\infty )$.