| Directions: In the given questions, two equations numbered I and II are given. Solve both the equations and mark the appropriate answer. |
| I. \[15{{x}^{2}}-29x-14=0\] |
| II. \[6{{y}^{2}}-5y-25=0\] |
A) \[x>y\]
B) \[x\ge y\]
C) \[x<y\]
D) \[x\le y\]
E) Relationship between x and y cannot be determined
Correct Answer: E
Solution :
| I. \[15{{x}^{2}}-29x-14=0\] |
| \[{{x}_{1}}=\frac{29+\sqrt{841+60\times 14}}{30}\] |
| \[=\frac{29+41}{30}=\frac{70}{30}=\frac{7}{3}\] |
| or \[{{x}_{2}}=\frac{29-\sqrt{1681}}{30}\] |
| \[\Rightarrow \] \[{{x}_{2}}=\frac{29-41}{30}=\frac{-12}{30}=\frac{-\,2}{5}\] |
| \[\Rightarrow \] \[x=\frac{7}{3},\]\[\frac{-\,2}{5}\] |
| II. \[6{{y}^{2}}-5y-25=0\] |
| \[{{y}_{1}}=\frac{5+\sqrt{25-4\times 6\times -25}}{12}\] |
| \[=\frac{5+\sqrt{625}}{12}=\frac{30}{12}=\frac{5}{2}\] |
| or \[{{y}_{2}}=\frac{5-\sqrt{25-4\times 6\times -\,25}}{12}\] |
| \[\Rightarrow \] \[{{y}_{2}}=\frac{5-\sqrt{625}}{12}=\frac{-\,20}{12}=\frac{-\,5}{3}\] |
| \[\Rightarrow \] \[y=\frac{5}{2},\]\[\frac{-\,5}{3}\] |
| So, relationship between x and y cannot be determined. |
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