If S`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-alpha)^(2)(gamma-alpha)^(2)`

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 alpha, beta, gamma are the roots of the cubic equation x^(3)+qx+r=0 then the find equation whose roots are (alpha-beta)^(2),(beta-gamma)^(2),(gamma-alpha)^(2) .

If |(alpha^(2n),alpha^(2n+2),alpha^(2n+4)),(beta^(2n),beta^(2n+2),beta^(2n+4)),(gamma^(2n),gamma^(2n+2),gamma^(2n+4))|=((1)/(beta^(2))-(1)/(alpha^(2)))((1)/(gamma^(2))-(1)/(beta^(2)))((1)/(alpha^(2))-(1)/(gamma^(2))) {where alpha^(2), beta^(2) and gamma^(2) are al distinct}, then the value of n 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 alpha^(2)beta+alpha^(2)gamma+beta^(2)alpha+beta^(2)gamma+gamma^(2)alpha+gamma^(2)beta is equal to

For alpha, beta, gamma in R , let A=[(alpha^(2),6,8),(3,beta^(2),9),(4,5,gamma^(2))] and B=[(2alpha,3,5),(2,2beta,6),(1,4,2gamma-3)]

If S_(1),S_(2),S_(3) be respectively the sum of n, 2n and 3n terms of a GP, then (S_(1)(S_(3)-S_(2)))/((S_(2)-S_(1))^(2)) is equal to

If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + r = n then the value of (alpha - 1/(beta gamma)) (beta -1/(gamma alpha)) (gamma-1/(alpha beta)) is:

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

If S_(1)=alpha^(2)+beta^(2)-a^(2) , then angle between the tangents from (alpha, beta) to the circle x^(2)+y^(2)=a^(2) , is

If alpha , beta are the roots of the equation ax^(2)+bx+c=0 and S_(n)=alpha^(n)+beta^(n) , then aS_(n+1)+bS_(n)+cS_(n-1)=(n ge 2)