Matrices and Determinants: JEE Main 2019 Mathematics 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: