`alpha` is root of `x^2+x+1` then sum of terms in expansion of `(1+alpha)^7=a+b alpha+ c alpha^2` then `5(3a-2b-c)`

If alpha!=1 is an n^(th) root of unity and n in N such thatfirst three terms in the expansion of (alpha+x)^(n) are 1,alpha and (n-1)/(2n)bar(a)^(2), then the value of x, is

If ac

If the sum of the coefficient in the expansion of (alpha x^(2) - 2x + 1)^(35) is equal to the sum of the coefficient of the expansion of (x - alpha y)^(35) , then alpha =

If alpha satisfies the equation x^(2)+x+1=0 and (1+alpha)^(7)=A+B alpha+C alpha^(2) , A,B,C ge 0 , then 5(3A-2B-C) is equal to

If alpha is an imaginary roots of x^(5)-1=0, then the equation whose roots are alpha+alpha^(4) and alpha^(2)+alpha^(3) is

If alpha is a root of the equation 4x^(2)+2x-1=0 then the other root is given by O -2 alpha-1 O 4 alpha^(2)+alpha-1 O 4 alpha^(3)-3 alpha O 4 alpha^(2)-3 alpha

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

Let alpha be a root of the equation x ^(2) - x+1=0, and the matrix A=[{:(1,1,1),(1, alpha , alpha ^(2)), (1, alpha ^(2), alpha ^(4)):}] and matrix B= [{:(1,-1, -1),(1, alpha, - alpha ^(2)),(-1, -alpha ^(2), - alpha ^(4)):}] then the vlaue of |AB| is:

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