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Let p(x) =x^6-x^5-x^3-x^2-x and alpha, b...

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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