| Directions: In the following questions, two equations numbered I and II have been given. You have to solve both the equation and mark the correct answer. [IBPS (PO) Pre 2011] |
| I. \[2{{x}^{2}}+23x+63=0\] |
| II. \[4{{y}^{2}}+19y+21=0\] |
A) \[x<y\]
B) \[x>y\]
C) \[x\ge y\]
D) \[x\le y\]
E) Relationship between x and y cannot be Established
Correct Answer: A
Solution :
| I. \[2{{x}^{2}}+23x+63=0\] |
| \[\Rightarrow \]\[2{{x}^{2}}+14x+9x+63=0\] |
| \[\Rightarrow \]\[2x\,\,(x+7)+9\,\,(x+7)=0\] |
| \[\Rightarrow \]\[(x+7)(2x+9)=0\] |
| \[\Rightarrow \]\[x=-7,\]\[x=-\frac{9}{2}\] |
| II. \[4{{y}^{2}}+19y+21=0\] |
| \[\Rightarrow \]\[4{{y}^{2}}+12y+7y+21=0\] |
| \[\Rightarrow \]\[4y\,(y+3)+7\,(y+3)=0\] |
| \[\Rightarrow \] \[(y+3)(4y+7)=0\] |
| \[\therefore \]\[y=-\,3,\]\[y=-\frac{7}{4}\] |
| Hence, \[y>x\] |
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