JEE Math Practice Question

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

1. A.$$\lambda $$2 + $$\lambda $$ - 6 = 0
2. B.$$\lambda $$2 - $$\lambda $$ - 6 = 0
3. C.$$\lambda $$2 - 3$$\lambda $$ - 4 = 0
4. D.$$\lambda $$2 + 3$$\lambda $$ - 4 = 0