A) \[0\]
B) \[\pm 1\]
C) \[\pm 7\]
D) \[49\]
Correct Answer: C
Solution :
We have the expression \[2{{x}^{2}}+mxy+3{{y}^{2}}-5y-2\] Comparing the given expression with \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c,\] We get, \[a=2,\,h=\frac{m}{2},\,b=3,\,c=-2,\,g=0,\,f=-\frac{5}{2}\] The given expression is resolvable into linear factors, if \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\] \[(2)\,(3)\,(-2)+2(0)-2\left( \frac{25}{4} \right)-0-(-2)\frac{{{m}^{2}}}{4}=0\] \[\Rightarrow \] \[-12-\frac{25}{2}+\frac{{{m}^{2}}}{2}=0\] \[\Rightarrow \] \[\frac{{{m}^{2}}}{2}=\frac{49}{2}\] \[\Rightarrow \] \[{{m}^{2}}=49\] \[\Rightarrow \] \[m=\pm 7\]
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