| Directions: In these questions two equations numbered I and II are given. |
| You have to solve both the equations and give answer. |
| I. \[{{x}^{2}}+10x+24=0\] |
| II. \[4{{y}^{2}}-17y+18=0\] |
A) If \[x\le y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x>y\]
E) If relationship between x and .y cannot be established
Correct Answer: C
Solution :
| I. \[{{x}^{2}}+10x+24=0\] |
| \[\Rightarrow \]\[{{x}^{2}}+6x+4x+24=0\] |
| \[\Rightarrow \]\[x\,\,(x+6)+4\,\,(x+6)=0\] |
| \[\Rightarrow \] \[(x+4)(x+6)=0\] |
| \[\therefore \] \[x=-\,\,4,\]\[-\,\,6\] |
| II. \[4{{y}^{2}}-17y+18=0\] |
| \[\Rightarrow \]\[4{{y}^{2}}-8y-9y+18=0\] |
| \[\Rightarrow \]\[4y\,\,(y-2)-9\,\,(y-2)=0\] |
| \[\Rightarrow \] \[(4y-9)(y-2)=0\] |
| \[\therefore \] \[y=\frac{9}{4},\]\[2\] |
| Hence, \[x<y\] |
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