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Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B ...

Let `|(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot` Then the value of `5A+4B+3C+2D+E` is equal to a. zero b. `-16` c. `11` d. `-11`

A

`0`

B

`-16`

C

`16`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`|(x,2,x),(x^(2),x,6),(x,x,6)|`
`= |(x,2,x),(x^(2),x,6),(x -x^(2),0,0)| " " ["Applying " R_(3) rarr R_(3) - R_(2)]`
`= (x -x^(2)) (12 -x^(2))`
`= 12 x - x^(3) - 12x^(2) + x^(4)`
`:. a =1, b = -1, c = -12, d = 12 and e = 0`
`:. 5a + 4b + 3c + 2d + e = 5 - 4 - 36 + 24 + 0 = -11`
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