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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» 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` |
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