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Q.

Let λbe 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

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a

λ2−3λ−4=0

b

λ2−λ−6=0

c

λ2+3λ−4=0

d

λ2+λ−6=0

answer is B.

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Detailed Solution

The condition for a non-homogeneous system of equation to have infinitely many solutions is Δ=Δ1=Δ2=Δ3=0⇒1114λ-λ32-4=0⇒8λ=24 ⇒ λ=3λ=3is a root of λ2−λ−6=0

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