| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. [RBI (Assistant) Scale 2011] |
| I. \[{{x}^{2}}+5x+6=0\] |
| II. \[{{y}^{2}}+3y+2=0\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If \[x=y\] or the relationship cannot be established
Correct Answer: D
Solution :
| I. \[{{x}^{2}}+5x+6=0\] |
| \[\Rightarrow \]\[{{x}^{2}}+2x+3x+6=0\]\[\Rightarrow \]\[x\,\,(x+2)+3\,\,(x+2)=0\] |
| \[\Rightarrow \]\[(x+3)(x+2)=0\]\[\Rightarrow \]\[x=-\,\,3,\]\[-\,\,2\] |
| II. \[{{y}^{2}}+3y+2=0\] |
| \[\Rightarrow \]\[{{y}^{2}}+2y+y+2=0\]\[\Rightarrow \]\[y\,\,(y+2)+1\,\,(y+2)=0\] |
| \[\Rightarrow \]\[(y+1)(y+2)=0\]\[\Rightarrow \]\[y=-\,\,1,\]\[-\,\,2\] |
| Hence, \[x\le y.\] |
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