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If the equation |x^2-5x + 6|-lambda x+7...

If the equation `|x^2-5x + 6|-lambda x+7 lambda=0` has exactly 3 distinct solutions then `lambda` is equal to

A

`-7+sqrt(23)`

B

`-9+4sqrt(5)`

C

`-7-sqrt(23)`

D

`-9-4sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `|x^(2)-5x+6|-lambdax+7lambda=0` has exactly three solutions,
`:.` as shown in the graph
`-x^(2)+5x-6=lambdax-7lambda` must have equal roots

`:.x^(2)+(lambda-5)x+6-7lambda=0` has discriminant zero
`implieslambda=-9+4sqrt(5)`
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