What are the characteristics (a, b, c and `alpha, beta, gamma`) values in a tetragonal systems)

Show that (a^2) /( x- alpha) +( b^2)/( x -beta) +(c^2)/( x- gamma)- x + delta =0 has only real roots if a ,b,c , alpha , beta , gamma , delta are all real .

cos alpha + cos beta + cos gamma + cos ( alpha + beta + gamma ) =

Assertion (A): White tin is an example of tetragonal system. Reasoning (R): For a tetragonal system a = b = c and a = p = y * 90^@ .

If alpha,beta, gamma are any three angles , then cos alpha + cos beta - cos gamma - cos (alpha+beta+gamma)=

If alpha , beta are the roots of x^2+ax -b=0 and gamma , sigma are the roots of x^2 + ax +b=0 then (alpha - gamma )(beta - gamma )( alpha - sigma )( beta - sigma )=

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 roots of a cubic polynomial then alpha beta gamma =……

alpha, beta, gamma are the root of x^(3)-2x^(2)-x+2=0 . Centroid of triangle with verties alpha, beta, gamma, (beta, gamma, alpha), (gamma, alpha, beta) is