Let λ  be a real number for which the system of linear equations  x+y+z=6,4x+λy−λz=λ−2and  3x+2y−4z=−5 has infinitely many solutions . Then   is a root of the quadratic equation

Given, system of linear equations x+y+z=64x+λy−λz=λ−2 And  3x+2y−4z=−5 Has infinitely manv solutions then Δ=0⇒1114λ−λ32−4=0⇒1(−4λ+2λ)−1(−16+3λ)+1(8−3λ)=0⇒−8λ+24=0⇒λ=3 From the options λ=3. satisfy the quadratic equation λ2−λ−6=0