Which of the following is not the root of the equation `|x-6-1 2-3xx-3-3 2xx+2|=0?` `2` b. `0` c. `1` d. `-3`

Options

A. 2
B. 0
C. 1
D. -3

Answer

B

Explanation

Operation `R_(1) to R_(1)-R_(2)` gives
`Delta =|{:(x-2,,3(x-2),,-(x-2)),(2,,-3x,,x-3),(-3,,2x,,x+2):}|`
`=(x-2)|{:(1,,3,,-1),(2,,-3x,,x-3),(-3,,2x,,x+2):}|`
`=(x-2) |{:(1,,3,,-1),(0,,-3(x+2),,x-1),(0,,2x+9,,x-1):}|" " underset(R_(3) to R_(3) +3R_(1)]([R_(2) to R_(2) -2R_(1)]]`
`=(x-2){-(3x+6)(x-1)-(x-1)(2x+9)}`
`=-(x-2)(x-1) (5x+15)`
Therefore `Delta =0 " gives " x=2 ,1,=3`