If `|(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2` then the ordered pair (A,B) is equal to

Options

A. `(4,5)`
B. `(-4,-5)`
C. `(-4,3)`
D. `(-4,5)`

Answer

D

Explanation

`Delta = |{:(x-4,,2x,,2x),(2x,,x-4,,2x),(2x,,2x,,x-4):}|`
Applying `C_(1) to C_(1)+C_(2)+C_(3)` we get
`Delta = |{:(5x-4,,2x,,2x),(5x-4,,x-4,,2x),(5x-4,,2x,,x-4):}|`
Applying `R_(1) to R_(1)- R_(2) " and " R_(2) to R_(2) -R_(2) ` we get
`Delta = |{:(0,,x+4,,0),(0,,-x-4,,x+4),(5x-4,,2x,,x-4):}|`
Expanding `C_(1)` we get
`Delta =(5x -4) (x+4)^(2)`
`:. A -4 ,B=5`