If x2 +2x +2xy + my - 3 -0 has two rational factors then the values of m will be

Given expression x2+2x+2xy+my−3=0 can be rewritten as x2+2x(1+y)+(my−3)=0But factors are rational ,so discriminant b2 - 4ac is a perfect square.Now, b2−4ac=4(1+y)2−(my−3)≥0⇒        4y2+1+2y−my+3    ≥0⇒        y2+2y−my+4    ≥0Now, taking (-) ve sign, we get m = 6for +ve sign , we get m=-2