| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[2{{x}^{2}}+11x+14=0\] |
| II. \[4{{y}^{2}}+12y+9=0\] |
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: C
Solution :
| I. \[2{{x}^{2}}+11x+14=0\] |
| \[\Rightarrow \]\[2{{x}^{2}}+7x+4x+14=0\] |
| \[\Rightarrow \]\[x\,\,(2x+7)+2\,\,(2x+7)=0\] |
| \[\Rightarrow \] \[(x+2)(2x+7)=0\] |
| \[\Rightarrow \] \[x=-\,2,\]\[-\frac{7}{2}\] |
| II. \[4{{y}^{2}}+12y+9=0\] |
| \[\Rightarrow \]\[4{{y}^{2}}+6y+6y+9=0\] |
| \[\Rightarrow \]\[2y\,\,(2y+3)+3\,\,(2y+3)=0\] |
| \[\Rightarrow \]\[(2y+3)(2y+3)=0\]\[\Rightarrow \]\[y=-\,\,\frac{3}{2},\]\[-\frac{3}{2}\] |
| \[\therefore \]\[x<y\] |
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