Question

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<br>A. non-negative
B. non- positive
C. begative
D. positive

Answer 1

Correct Answer - 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`