Let  $\lambda$ be a real number for which the system of linear equations x+y+z=6, $4x+\lambda y-\lambda z=\lambda -2 \text{and }3x+2y-4z=-5\text{ has infinitely many solutions. Then }\lambda \text{ is a root of the }$equation

• A

  ${\lambda }^2-3\lambda -4=0$

• B

  ${\lambda }^2+3\lambda -4=0$

• C

  ${\lambda }^2-\lambda -6=0$

• D

  ${\lambda }^2+\lambda -6=0$