A) \[\left( \frac{1}{13},\frac{1}{3} \right)\]
B) \[\left[ -\frac{1}{13},\frac{1}{3} \right]\]
C) \[\left( -\frac{1}{3},\frac{1}{13} \right)\]
D) None of these
Correct Answer: B
Solution :
If the given expression be y, then \[y=2{{x}^{2}}y+(3y-1)x+(6y-2)=0\] If \[y\ne 0\]then \[\Delta \ge 0\]for real x i.e. \[{{B}^{2}}-4AC\ge 0\] or - \[39{{y}^{2}}+10y+1\ge 0\] or \[(13y+1)(3y-1)\le 0\] Þ \[-1/13\le y\le 1/3\] If \[y=0\] then \[x=-2\] which is real and this value of \[y\] is included in the above range.
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