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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)=`

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The correct Answer is:
6
`Q(x)=(x^(3)-2x^(2)+x-1)(x+1)=0impliesdelta=-1`
`alpha+ beta+gamma=2, alpha beta+beta gamma +gamma alpha=1`
`p(x)=(x^(2)+1)Q(x)+x^(2)-x+1`
`p(alpha)+p(beta)+p(gamma)+p(-1)=alpha^(2)+beta^(2)+gamma^(2)+1-(alpha+beta+gamma-1)+4`
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