| Directions: In these questions two equations numbered I and II are given. You have to solve both the equations and find the correct option. |
| I. \[4{{x}^{2}}-29x+45=0\] |
| II. \[3{{y}^{2}}-19y+28=0\] |
A) \[x<y\]
B) \[x>y\]
C) \[k\ge y\]
D) \[k\le y\]
E) Relationship between x and y cannot be established
Correct Answer: E
Solution :
| I. \[4{{x}^{2}}-29x+45=0\] |
| \[\Rightarrow \]\[4{{x}^{2}}-20x-9x+45=0\] |
| \[\Rightarrow \]\[4x\,\,(x-5)-9\,\,(x-5)=0\] |
| \[\Rightarrow \]\[(4x-9)(x-5)=0\]\[\Rightarrow \]\[x=5,\]\[x=\frac{9}{4}\] |
| II. \[3{{y}^{2}}-19y+28=0\] |
| \[\Rightarrow \]\[3{{y}^{2}}-12y-7y+28=0\] |
| \[\Rightarrow \]\[3y\,\,(y-4)-7\,\,(y-4)=0\] |
| \[\Rightarrow \]\[(3y-7)(y-4)=0\]\[\Rightarrow \]\[y=4,\]\[y=\frac{7}{3}\] |
| Hence, relationship between x and y cannot be established. |
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