| Directions: In the given questions two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. [NICL (AO) 2014] |
| I. \[3{{x}^{2}}-26x-29=0\] |
| II. \[6{{y}^{2}}-15y+25=0\] |
A) \[x\ge y\]
B) \[x<y\]
C) \[x>y\]
D) \[x\le y\]
E) relationship between x and y cannot be determined
Correct Answer: E
Solution :
| I. \[3{{x}^{2}}-26x-29=0\] |
| \[\Rightarrow \]\[3{{x}^{2}}-29x+3x-29=0\] |
| \[\Rightarrow \]\[x\,(3x-29)+1\,(3x-29)=0\] |
| \[\Rightarrow \]\[(3x-29)(x+1)=0\]\[\Rightarrow \]\[x=\frac{29}{3},\]\[-1\] |
| II. \[6{{y}^{2}}-25y+25=0\] |
| \[\Rightarrow \]\[6{{y}^{2}}-15y-10y+25=0\] |
| \[\Rightarrow \]\[3y\,(2y-5)-5\,(2y-5)=0\] |
| \[\Rightarrow \] \[(2y-5)(3y-5)=0\] |
| \[\Rightarrow \] \[y=\frac{5}{2},\]\[y=\frac{5}{3}\] |
| \[\therefore \] Relationship between x and y can't be determined. |
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