If `alpha, beta, gamma` are the 3 positive roots of cubic `x^3-ax^2+bx-16sqrt6=0` then the minimum value of `(4/(alphabeta)+3/(betagamma)+2/(alphagamma))` is

If alpha,beta,gamma are the 3 positive roots of cubic x^(3)-ax^(2)+bx-16sqrt(6)=0 then the x^(3)-ax^(2)+bx-16sqrt(6)=0 then the minimum value of ((4)/(alpha beta)+(3)/(beta gamma)+(2)/(alpha gamma)) is

If alpha, beta and gamma are the roots of the equation x^(3)-px^(2)+qx-r=0 , then the value of (alphabeta)/(gamma)+(betagamma)/(alpha)+(gammaalpha)/(beta) is equal to

If alpha, beta and gamma are the roots of the equation x^(3)-px^(2)+qx-r=0 , then the value of (alphabeta)/(gamma)+(betagamma)/(alpha)+(gammaalpha)/(beta) is equal to

If alpha , beta , gamma are the roots of x^3 -3ax^2 +3 bx -c=0 which are in H.P then beta =

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, then find he value of (alpha-1/(betagamma))(beta-1/(gammaalpha))(gamma-1/(alphabeta)) .

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