The equation represents a pair of lines if 1⋅1⋅4+2⋅f⋅g⋅1−1⋅f2−1⋅g2−4⋅12=0 ⇒(f−g)2=0⇒f=g The equation becomes (x+y)2+2g(x+y)+4=0 Which represents pair of parallel lines, which are real provided (2g)2−4⋅4⋅1≥0⇒|g|≥2