| Directions: In the following questions, two equations numbered I and II have been given. You have to solve both the equations and mark the correct answer. |
| I. \[2{{x}^{2}}+23x+63=0\] |
| II. \[4{{y}^{2}}+19y+21=0\] |
A) If \[x<y\]
B) If \[x>y\]
C) If \[x\ge y\]
D) If \[x\le y\]
E) If 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. \[4{{y}^{2}}+19y+21=0\] |
| \[\Rightarrow \]\[4{{y}^{2}}+12y+7y-21=0\] |
| \[\Rightarrow \]\[4y\,\,(y+3)+7\,\,(y+3)=0\] |
| \[\Rightarrow \] \[(y+3)(4y+7)=0\] \[\Rightarrow \] \[y=-\,\,3,\]\[y=-\frac{7}{4}\] |
| \[\therefore \] \[y>x\] |
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