Find the values of `m` for which the expression `2x^2+m x y+3y^2-5y-2` can be resolved into two rational linear factors.

Explanation

We know that `ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c` can be resolved into two linear factors if and only if
` abc + 2fgh - af^(2) - bg^(2) -ch^(2) = 0`
Given expression is
`2x^(2) + mxy + 3y^(2) - 5y - 2`
Here, `a = 2, h = m//2` ,
`b = 3 ,g = 0` ,
`f = - 5//2,`
`c = -2`
Therefore, expression `2x^(2) + mxy + 3y^(2) - 5y - 2` will have two linear factors if and only if
or `2xx3(-2) + 2 ((-5)/(2))(0) ((m)/(2))-2 ((-5)/(2))^(2) - 3 xx0^(2) - (-2)((m)/(2))^(2) =0`
or `-12 - (25)/(2) + (m^2)/(2) =0`
or ` m^(2) = 49`
or ` m = pm 7`