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Let lambda be a real number for which th...

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

A

`lamda^(2) + 3 lamda -4 = 0`

B

`lamda^(2) - lamda -6 = 0`

C

`lamda^(2) + lamda -6 = 0`

D

`lamda^(2) - 3 lamda - 4 = 0`

Text Solution

Verified by Experts

The correct Answer is:
B
For infinitely many solution which satisfies
`Delta = Delta_(1) = Delta_(2) = Delta_(3) = 0`
`Delta = 0 rArr |(1,1,1),(4,lamda,-lamda),(3,2,-4)|= 0 rArr lamda = 3` which satisfies `lamda^(2) - lamda - 6 = 0`
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