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If P(x)=x^(6)-x^(5)-x^(3)-x^(2)-x & alph...

If `P(x)=x^(6)-x^(5)-x^(3)-x^(2)-x` & `alpha, beta, gamma, delta` are the roots of the equation `Q(x)=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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