If `alpha` is a root of `x^3-x-1=0`, compute the value of `alpha^10 + 2alpha^8-alpha^7-3alpha^6-3alpha^5+4alpha^4+2alpha^3-4alpha^2-6alpha`.

If alpha is a root of x^(4) + x^(2) - 1 = 0 , the value of (alpha^(6) + 2 alpha^(4))^(2012) is

If alpha be a root of equation x^2+x+1=0 then find the vlaue of (alpha+ 1/alpha)+(alpha^2+1/alpha^2)^2+(alpha^3+1/alpha^3)^2+…+(alpha^6+1/alpha^6)^2

If alpha be a root of equation x^2+x+1=0 then find the vlaue of (alpha+ 1/alpha)+(alpha^2+1/alpha^2)^2+(alpha^3+1/alpha^3)^2+…+(alpha^6+1/alpha^6)^2

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

If alpha is root of equation f(x)=0 then the value of (alpha+ 1/alpha)^2+(alpha^2+ 1/alpha^2)^2+(alpha^3+1/alpha^3)+………+(alpha^6+ 1/alpha^6)^2 is (A) 18 (B) 54 (C) 6 (D) 12

IF alpha is a root of the equation 4x ^2 +2x-1=0 then 4 alpha ^3 - 3 alpha is

If alpha is a non-real root of x^(7) = 1 then alpha (1 + alpha)(1 + alpha^(2) + alpha^(4))=

If alpha is a non-real root of x^(7) = 1 then alpha(1 + alpha) (1 + alpha^(2) + alpha^(4)) =

If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+alpha^(3)+alpha^(4)+alpha^(5))/(alpha+1)