The value of `|{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalpha,gammaalpha'+gamma'alpha,gamma'alpha'),(alphabeta,alphabeta'+alpha'beta,alpha'beta'):}|` is

If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value of the determinant |(alphabeta,betagamma,gammaalpha),(betagamma,gammaalpha,alphabeta),(gammaalpha,alphabeta,betagamma)| is a. p b. q c. 0 d. r

If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value of the determinant |(alphabeta,betagamma,gammaalpha),(betagamma,gammaalpha,alphabeta),(gammaalpha,alphabeta,betagamma)| is p b. q c. 0 d. r

Prove that |2alpha+beta+gamma+deltaalphabeta+gammadeltaalpha+beta+gamma+delta2(alpha+beta)(gamma+delta)alphabeta(gamma+delta)+gammadelta(alpha+beta)alphabeta+gammadeltaalphabeta(gamma+delta)+gammadelta(alpha+beta)2alphabetagammadelta|=0

Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+gamma+delta2(alpha+beta)(gamma+delta)alphabeta(gamma+delta)+gammadelta(alpha+beta) alphabeta+gammadeltaalphabeta(gamma+delta)+gammadelta(alpha+beta)2alphabetagammadelta|=0

Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,gamma+alpha,alpha+beta]|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma) .

Using properties of determinants. Prove that |(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta)|=(beta-gamma)(gamma-alpha)(alpha-beta)(alpha+beta+gamma)

Evaluate the following: |[1,1,1],[alpha, beta, gamma],[beta gamma, gamma alpha, alpha beta]|

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)