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 infinitely many solutions. Then λ is a root of the quadratic equation :

Let λ be a real number for which the system of linear equations x+y+z=6,4x+λyλz=λ2,3x+2y4z=5 has infinitely many solutions. Then λ is a root of the quadratic equation :

  1. A

    λ2λ6=0

  2. B

    λ23λ4=0

  3. C

    λ2+λ6=0

  4. D

    λ2+3λ4=0

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    Solution:

    For infinitely many solutions

    1114λλ324=0 1(4λ+2λ)1(16+3λ)+1(83λ)=0 2λ+163λ+83λ=08λ+24=0λ=3

    Putting λ=3 is λ2λ6, we get

    λ2λ6=936=0

     λ=3 is a root of the quadratic equation

    λ2λ6=0.

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