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

Options

A. non-negative
B. non- positive
C. begative
D. positive

Answer

C

Explanation

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`