| Directions: In each of the following questions two equations are given, solve these equations and give answer. [IBPS (PO) 2013] |
| I. \[{{x}^{2}}+5x+6=0\] |
| II. \[{{y}^{2}}+7y+12=0\] |
A) If \[x\ge y\]
B) If \[x>y\]
C) If \[x\le y\]
D) If \[x<y\]
E) If \[x=y\]
Correct Answer: A
Solution :
| I. \[{{x}^{2}}+5x+6=0\] |
| \[\Rightarrow \]\[{{x}^{2}}+2x+3x+6=0\] |
| \[\Rightarrow \]\[x\,\,(x+2)+3\,\,(x+2)=0\]\[\Rightarrow \]\[(x+3)(x+2)=0\] |
| \[\therefore \] \[x=-\,\,3,\]\[-\,\,2\] |
| II. \[{{y}^{2}}+7y+12=0\] |
| \[\Rightarrow \]\[{{y}^{2}}+3y+4y+12=0\] |
| \[\Rightarrow \]\[y\,\,(y+3)+4\,\,(y+3)=0\] |
| \[\Rightarrow \]\[(y+4)(y+3)=0\] |
| \[\therefore \] \[y=-\,\,3,\]\[-\,\,4\] |
| Hence, \[x\ge y\] |
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