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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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Answer» Correct Answer - 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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