alpha, beta, gamma में संबंध

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0 , then the value of |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is

If alpha, beta, gamma be the zeros of the polynomial p(x) such that (alpha+beta+gamma) = 3, (alpha beta+beta gamma+gamma alpha) =- 10 and alpha beta gamma =- 24 then p(x) = ?

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

If alpha, beta, gamma are the roots of ax ^ (3) + bx ^ (2) + cx + d = 0 and det [[alpha, beta, gammabeta, gamma, alphagamma, alpha, beta]] = 0, alpha ! = beta! = gamma, alpha + beta-gamma, beta + gamma-alpha, and gamma + alpha-beta

Let sin^(-1)alpha+sin^(-1)beta+sin^(-1)gamma=pi and alpha, beta, gamma are non zero real numbers such that (alpha+beta+gamma)(alpha+beta-gamma)=3alphabeta then value of gamma

If alpha, beta, gamma are the roots of x^3+px^2+qx+r=0 then alpha^(2)(beta+gamma)+beta^(2)(gamma+alpha)+gamma^(2)(alpha+beta)=