Number of real values of λ for which the system of equations λ+3x+λ+2y+z=0, 3x+λ+3y+z=0, 2x+3y+z=0 possess a non-trivial solution is

The necessary condition for a homogeneous system of equations to have a non-trivial solution is Δ=0⇒λ+3λ+213λ+31231=0     R1→R1-R2, R2→R2-R3⇒λ-101λ0231=0 ⇒λ(λ-0)+1(1-0)+03-2λ=0⇒λ2+1=0There is no real value for λ