| Directions: In each of the following questions two equations are given. Solve these equations and give answer. [IBPS (SO) 2013] |
| I. \[6{{x}^{2}}+77x+121=0\] |
| II. \[{{y}^{2}}+9y-22=0\] |
A) If \[x<y\]
B) If \[x>y\]
C) If \[x=y\]
D) If \[x\ge y\]
E) If \[x\le y\]
Correct Answer: E
Solution :
| I. \[6{{x}^{2}}+77x+121=0\] |
| \[\Rightarrow \]\[6{{x}^{2}}+66x+11x+121=0\] |
| \[\Rightarrow \]\[6x\,\,(x+11)+11\,\,(x+11)=0\] |
| \[\Rightarrow \]\[(6x+11)(x+11)=0\] |
| \[\therefore \]\[x=-11,\]\[-\frac{11}{6}\] |
| II. \[{{y}^{2}}+9y-22=0\] |
| \[\Rightarrow \]\[{{y}^{2}}+11y-2y-22=0\] |
| \[\Rightarrow \]\[y\,\,(y+11)-2\,\,(y+11)=0\]\[\Rightarrow \]\[(y-2)(y+11)=0\] |
| \[\therefore \]\[y=2,\]\[-\,\,11\] |
| Hence, \[x\le y\] |
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