Question

Let λ be a real number for which the system of linear equations
x + y + z = 6
4x + λy – λz = λ – 2
3x + 2y – 4z = –5
Has indefinitely many solutions. Then λ is a root of the quadratic equation
(A) λ²
– λ – 6 = 0 (B) λ²
– 3λ – 4 = 0 (C) λ² + 3λ – 4 = 0 (D) λ² + λ – 6 = 0

Answer 1

system of linear equations by determinant method;

make a determinant by the cofficeints of equations .

now put the determinat = 0

after solving u get

λ= 3

it satisfies the equation

λ² + λ – 6 = 0

so the correct option is d)