If `alpha,beta,gamma` are different from 1 and are the roots of `a x^3+b x^2+c x+d=0a n d(beta-gamma)(gamma-alpha)(alpha-beta)=(25)/2` , then prove that `|alpha/(1-alpha)beta/(1-beta)gamma/(1-gamma)alphabetagammaalpha^2beta^2gamma^2|=(25 d)/(2(a+b+c+d))`

If alpha,beta,gamma are different from 1 and are the roots of ax^(3)+bx^(2)+cx+d=0 and (beta-gamma)(gamma-alpha)(alpha-beta)=(25)/(2) ,then prove that det[[(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)(alpha)/(1-alpha),(beta)/(1-beta),(gamma)/(1-gamma)alpha,beta,gammaalpha^(2),beta^(2),gamma^(2)]]=(25d)/(2(a+b+c+d))

If alpha , beta , gamma are the roots of x^3 + 2x^2 + 3x +8=0 then ( alpha + beta ) ( beta + gamma) ( gamma + alpha ) =

If alpha , beta , gamma are the roots of x^3 + 2x^2 + 3x +8=0 then ( alpha + beta ) ( beta + gamma) ( gamma + alpha ) =

If alpha, beta, gamma are roots of x^(3)-2x^(2)+7x-1=0 then the value of (alpha+beta-gamma) (beta+gamma-alpha) (alpha+gamma-beta)

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

If alpha,beta,gamma are the roots of the equation x^3 + 4x +1=0 then (alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1)=

If alpha,beta,gamma are the roots of the equation x^3 + 4x +1=0 then (alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1)=

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+c x+d=0a n d|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,a n dgamma+alpha-betadot