| Directions: In the given questions two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. [NICL (AO) 2014] |
| I.\[2{{x}^{2}}+9x+7=0\] |
| II. \[2{{y}^{2}}+9y+10=0\] |
A) \[x\ge y\]
B) \[x<y\]
C) \[x>y\]
D) \[x\le y\]
E) relationship between x and y cannot be determined
Correct Answer: E
Solution :
| I. \[2{{x}^{2}}+9x+7=0\] |
| \[\Rightarrow \]\[2{{x}^{2}}+2x+7x+7=0\] |
| \[\Rightarrow \]\[2x\,(x+1)+7\,(x+1)=0\] |
| \[\Rightarrow \] \[(x+1)(2x+7)=0\Rightarrow x=-1,\]\[-\frac{7}{2}\] |
| II. \[2{{y}^{2}}+9y+10=0\] |
| \[\Rightarrow \]\[2{{y}^{2}}+5y+4y+10=0\] |
| \[\Rightarrow \]\[y\,(2y+5)+2\,(2y+5)=0\] |
| \[\Rightarrow \] \[(2y+5)(y+2)=0\]\[y-\frac{5}{2},\]\[-\,2\] |
| \[\therefore \] Relationship between x and y can't be determined. |
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