Directions : In these 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. \[40{{x}^{2}}-47x+12=0\] |
II. \[5{{y}^{2}}-51y+54=0\] |
A) If \[x\le y\]
B) lf \[x<y\]
C) If \[x>y\]
D) If relationship between x and y cannot be established
E) lf \[x\ge y\]
Correct Answer: B
Solution :
I. \[40{{x}^{2}}-47x+12=0\] |
By splitting the middle term, |
\[40{{x}^{2}}-32x+15x+12=0\] |
\[8x\,(5x-4)-3\,(5x-4)=0\] |
\[(8x-3)(5x-4)=0\,\,\Rightarrow \,\,x=\frac{3}{8},\]\[\frac{4}{5}\] |
II. \[5{{y}^{2}}-51y+54=0\] |
By splitting the middle term, |
\[5{{y}^{2}}-45y-6y+54=0\] |
\[5y\,(y-9)-6\,(y-9)=0\] |
\[(5y-6)(y-9)=0\,\,\Rightarrow \,\,y=\frac{6}{5},\]9 |
Hence, \[y>x\] |
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