| Directions: In the following questions, two equations numbered I and II have been given. You have to solve both the equation and mark the correct answer. [IBPS (PO) Pre 2011] |
| I. \[3{{x}^{2}}+23x+44=0\] |
| II. \[3{{y}^{2}}+20y+33=0\] |
A) \[x<y\]
B) \[x>y\]
C) \[x\ge y\]
D) \[x\le y\]
E) Relationship between x and y cannot be Established
Correct Answer: D
Solution :
| I. \[3{{x}^{2}}+23x+44=0\] |
| \[\Rightarrow \]\[3{{x}^{2}}+12x+11x+44=0\] |
| \[\Rightarrow \]\[3x\,\,(x+4)+11\,\,(x+4)=0\] |
| \[\Rightarrow \]\[(3x+11)(x+4)=0\] |
| \[\Rightarrow \]\[x=-\,\,4,\]\[x=-\frac{11}{3}\] |
| II. \[3{{y}^{2}}+20y+33=0\] |
| \[\Rightarrow \]\[3{{y}^{2}}+11y+9y+33=0\] |
| \[\Rightarrow \]\[y\,\,(3y+11)+3\,\,(3y+11)=0\] |
| \[\Rightarrow \]\[(3y+11)(y+3)=0\] |
| \[\Rightarrow \]\[y=-\,\,3,\]\[y=-\frac{11}{3}\] |
| Hence, \[y\ge x\] |
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