If `S_r = alpha^r + beta^r + gamma^r` then show that `|[S_0,S_1,S_2],[S_1,S_2,S_3],[S_2,S_3,S_4]| = (alpha-beta)^2(beta-gamma)^2(gamma-alpha)^2`

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(0),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(2),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

Show that |[1,alpha,alpha^2],[1,beta,beta^2],[1,gamma,gamma^2]|=(alpha-beta)(beta-gamma)(gamma-alpha)

If alpha, beta , gamma are the zeros of the polynomial x^(3) - px^(2) + qx - r then 1/(alpha beta) + 1/(beta gamma) + 1/(gamma alpha) = …………..

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

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

Consider Delta=|(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)| Show that Delta=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma) .