Find the value of `m` for which the expressiion `12x^(2)-10xy+2y^(2)+11x-5y+m` can be resolved into two rational linear factors.

Explanation

Comparing the given expression with
`ax^(2)+2hxy+by^(2)_2gx+2fy+c`, we have
`a=12, h=-5, b=2, g=11/2,f=(-5/2),c=m`
The given expression will have two linear factors if and only if
`abc+2fgh-af^(2)-bg^(2)-ch^(2)=0`
or `(12)(2)(m)(-5/2)(11/2)(-5)-(12)(-5/2)^(2)`
`-(2)(11/2)^(2)-(m)(-5)^(2)=0`
`implies24m+275/2-75-121/2-25m=0` or `m-2`