| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[{{x}^{2}}+11x+30=0\] |
| II. \[{{y}^{2}}+7y+12=0\] |
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. \[{{x}^{2}}+11x+30=0\] |
| \[\Rightarrow \] \[{{x}^{2}}+6x+5x+30=0\] |
| \[\Rightarrow \] \[x\,(x+6)+5\,(x+6)=0\] |
| \[\Rightarrow \] \[(x+6)(x+5)=0\] |
| \[\Rightarrow \] \[x=-\,6,\]\[-\,5\] |
| II. \[{{y}^{2}}+7y+12=0\] |
| \[\Rightarrow \] \[{{y}^{2}}+4y+3y+12=0\] |
| \[\Rightarrow \] \[y\,(y+4)+3\,(y+4)=0\] |
| \[\Rightarrow \] \[(y+4)(y+3)=0\] |
| \[\Rightarrow \] \[y=-\,4,-\,3\] |
| Hence, \[y>x\] |
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