Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an inde\ufb01nite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t

\r\n2−4n. In the \ufb01rst section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some speci\ufb01c values of Q and P.<\/p>\r\n","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 35, 2009"}