A) \[-6,-2\]
B) \[-6,2\]
C) \[6,-2\]
D) 6, 2
Correct Answer: C
Solution :
Given expression \[{{x}^{2}}+2x+2xy+my-3\] can be written as \[{{x}^{2}}+2x(1+y)+(my-3)\] But factors are rational, so \[{{B}^{2}}-4AC\] is a perfect square. Now \[4\left\{ {{(1+y)}^{2}}-(my-3) \right\}\ge 0\] Þ\[4\left\{ {{y}^{2}}+1+2y-my+3 \right\}\ge 0\]Þ \[{{y}^{2}}+2y-my+4\ge 0\] Hence \[2y-my=\pm 4y\] {as it is perfect square} Þ \[2y-my=4y\Rightarrow m=-2\]. Now taking (-) sign, we get \[m=6\].
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