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VITEEE 2010 Paper

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Question : 89 of 120

Marks: +1, -0

For what values of m can the expression

2x^{2}+mxy+3y^{2}-5y-2

be expressed as the product of two linear factors?

0
± 1
± 7
49

Solution:

The given expression is

2x^{2}+mxy+3y^{2}-5y-2

Comparing the given expression with

ax^{2}+2hxy+by^{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-af^{2}-bg^{2}-ch^{2}=0

(2)(3)(-2)+2(0)-2\left(\frac{25}{4}\right)-0-(-2)\frac{m^{2}}{4}=0

⇒

-12-\frac{25}{2}+\frac{m^{2}}{2}=0

⇒

\frac{m^{2}}{2}=\frac{49}{2}

\Rightarrow m^{2}=49

⇒

m=\pm 7

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