if `alpha,beta,gamma` are non-real numbers satisfying `x^3-1=0,` then the value of `|[lambda+1,alpha,beta],[alpha,lambda+beta,1],[beta,1,lambda+1]|`

If alpha, beta are non - real numbers satisfying x^3-1=0 , then the value of : |(lamda+1,alpha,beta),(alpha,lamda+beta,1),(beta,1,lamda+alpha)| is equal to :

If alpha,beta and gamma are roots of x^(3) -2x+1=0,then the value of Sigma((1)/(alpha+beta-gamma)) is

If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+alpha)/(1-alpha)+(1+beta)/(1-beta)+(1+gamma)/(1-gamma) is equal to

If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+alpha)/(1-alpha)+(1+beta)/(1-beta)+(1+gamma)/(1-gamma) is equal to

If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+alpha)//(1-alpha)+(1+beta)//(1-beta)+(1+gamma)//(1-gamma) is equal to

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0, then the value of (alpha-(1)/(beta gamma))(beta-(1)/(gamma alpha))(gamma-(1)/(alpha beta)) is

If (alpha, beta, gamma) are roots of equation x^(3)-3x^(2)+1=0 then the value of [((alpha)/(1+alpha))^(3)+((beta)/(1+beta))^(3)+((gamma)/(1+gamma))^(3) is k then |k|=

If alpha,beta and gamma are the roots of x^(3)-x^(2)-1=0, then value of (1+alpha)/(1-alpha)+(1+beta)/(1-beta)+(1+gamma)/(1-gamma) is