Directions: In these questions two equations numbered I and II are given. |
You have to solve both the equations and give answer. |
I. \[6{{x}^{2}}+41x+63=0\] |
II. \[4{{y}^{2}}+8y+3=0\] |
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. \[6{{x}^{2}}+41x+63=0\] |
\[\Rightarrow \]\[6{{x}^{2}}+27x+14x+63=0\] |
\[\Rightarrow \]\[3x\,\,(2x+9)+7(2x+9)=0\] |
\[\Rightarrow \] \[(3x+7)(2x+9)=0\] |
\[\therefore \] \[x=-\frac{7}{3}x=-\frac{9}{2}\] |
II. \[4{{y}^{2}}+8y+3=0\] |
\[\Rightarrow \] \[4{{y}^{2}}+6y+2y+3=0\] |
\[\Rightarrow \]\[2y\,\,(2y+3)+1\,\,(2y+3)=0\] |
\[\Rightarrow \] \[(2y+1)(2y+3)=0\] |
\[\therefore \] \[y=-\frac{1}{2},\]\[-\frac{3}{2}\] |
Hence, \[x<y\] |
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