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Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2)...

Let `P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, delta` are the roots of the equation `x ^(4) -x ^(3)-x ^(2) -1=0,` then `P (alpha ) + P (beta) +P (gamma) + P(delta)=`

A

`4`

B

`6`

C

`8`

D

`12`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `P(x)=x^(6)-x^(5)-x^(3)-x^(2)-x` and `Q(x)=x^(4)-x^(3)-x^(2)-1`
Here` P(x)=Q(x)(x^(2)+1)+x^(2)-x+1`
`:. sumP(alpha)=sumalpha^(2)-sumalpha+4`
`=(sumalpha)^(2)-2sum(alphabeta)-sumalpha+4`
`=1-2(-1)-(1)+4`
`=6`
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