Question

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`

Answer 1

Correct Answer - 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`