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