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Let x<1, then value of |x^2+2 2x+1 1 2x+...

Let `x<1,` then value of `|x^2+2 2x+1 1 2x+1x+2 1 3 3 1|` is a. none-negative b. none-positive c. negative`` d. positive

A

non-negative

B

non- positive

C

begative

D

positive

Text Solution

Verified by Experts

The correct Answer is:
C
Applying `R_(1) to R_(1)-R_(2) " and " R_(2) to R_(2) to R_(2) -R_(3) ` reduce the determinant to
`|{:(x^(2)-2x+1,,x-1,,0),(2x-2,,x-1,,0),(3,,3,,1):}| =(x-1)^(3) -2(x-1)^(2)`
`=(x-1)^(2) (x-1-2)`
`=(x-1)^(2) (x-3)`
Which is clearly negative for `x lt 1`
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