Verified Solution • 2025–26 Session moderate

QJEEM19Mac57a: JEE Main 2019 Mathematics - Class 12 JEEM19Mac57a Solution: Let be a real number for which the system of linear equations x …

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

Multiple Choice Options

  • A λ\lambda 2 + λ\lambda - 6 = 0
  • B λ\lambda 2 - λ\lambda - 6 = 0
  • C λ\lambda 2 - 3 λ\lambda - 4 = 0
  • D λ\lambda 2 + 3 λ\lambda - 4 = 0

Step-by-Step Verified Solution

Δ=0\Delta = 0

|1114λ−λ32−4|=0

On solving we get λ\lambda = 3

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