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 roots of the equation ax^(2)+bx+c=0 are (alpha)/(alpha-1) and (alpha+1)/(alpha) and then (a+b+c)^(2) equals

If alpha,beta are the roots of the equation ax^(2)+bx+c=0, then (alpha)/(alpha beta+b)+(beta)/(a alpha+b) is equal to -

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)

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 the roots of equation x^(3) + ax^(2) + b = 0 are alpha _(1), alpha_(2), and alpha_(3) (a , b ne 0) . Then find the equation whose roots are (alpha_(1)alpha_(2)+alpha_(2)alpha_(3))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(2)alpha_(3)+alpha_(3)alpha_(1))/(alpha_(1)alpha_(2)alpha_(3)), (alpha_(1)alpha_(3)+alpha_(1)alpha_(2))/(alpha_(1)alpha_(2)alpha_(3)) .

if alpha and beta are the roots of the equation x^(2)+x+1=0 then alpha^(28)+beta^(28)=(A)1(B)-1(C)0(D)2

If alpha_(1),alpha_(2),alpha_(3), alpha_(4) are the roos of x^(4)+2x^(3)+bx^(2)+cx+d=0 such that alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2) , then b-c is equal to__________

I a, b and c are not all equal and alpha and beta be the roots of the equation ax^(2) + bx + c = 0 , then value of (1 + alpha + alpha^(2)) (1 + beta + beta^(2)) is