If `alpha, beta, gamma` are the roots of `x^(3)+px+q=0` then `|(alpha, beta, gamma),(beta, gamma, alpha),(gamma, alpha, beta)|=`

If alpha, beta, gamma are the roots of ax^(3) + bx^(2) + cx + d = 0 and |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| = 0, alpha != beta != gamma , then find the equation whose roots are alpha + beta - gamma, beta + gamma - alpha and gamma + alpha - beta

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

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

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 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 are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .

If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,beta,gamma],[beta,gamma,alpha],[gamma,alpha,beta]|=0, alpha!=beta!=gamma then find the equation whose roots are alpha+beta-gamma,beta+gamma-alpha , and gamma+alpha-beta .

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)=

If alpha,beta,gamma are roots of the equation x^(3)+px+q=0 then the value of |{:(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta):}| is