| Directions: In the given question two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. |
| I. \[{{x}^{2}}+7x+12=0\] |
| II. \[2{{y}^{2}}+11y+15=0\] |
A) If \[x\ge y\]
B) If \[x<y\]
C) If \[x>y\]
D) If \[x\le y\]
E) relationship between x and y cannot be determined
Correct Answer: D
Solution :
| I. \[{{x}^{2}}+7x+12=0\] |
| \[\Rightarrow \]\[{{x}^{2}}+4x+3x+12=0\] |
| \[\Rightarrow \]\[x\,(x+4)+3\,(x+4)=0\] |
| \[\Rightarrow \] \[(x+4)(x+3)=0\] |
| \[\Rightarrow \] \[x=-\,3,\]\[-\,4\] |
| II. \[2{{y}^{2}}+11y+15=0\] |
| \[\Rightarrow \]\[2{{y}^{2}}+6y+5y+15=0\] |
| \[\Rightarrow \]\[2y\,(y+3)+5\,(y+3)=0\] |
| \[\Rightarrow \] \[(y+3)(2y+5)=0\] |
| \[\Rightarrow \] \[y=-\,3,\]\[-\frac{5}{2}\] |
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