यदि बहुपद `p(x) = x^(3) + bx^(2) + cx + d ` के शून्यक `alpha beta" और " gamma` हों ताकि `alpha + beta+ gamma = - 4, alpha beta + beta gamma + alpha gamma = 3 " और " alpha beta gamma = 5 `,तो p(x) ज्ञात कीजिए ।

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

sin (beta+ gamma- alpha) + sin (gamma+ alpha - beta) + sin (alpha + beta- gamma)- sin (alpha + beta + gamma)=

sin (beta+ gamma- alpha) + sin (gamma+ alpha - beta) + sin (alpha + beta- gamma)- sin (alpha + beta + gamma)=

If alpha, beta, gamma be the zeros of the polynomial p(x) such that (alpha+beta+gamma) = 3, (alpha beta+beta gamma+gamma alpha) =- 10 and alpha beta gamma =- 24 then p(x) = ?

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 the roots of x^3 +px^2 +qx +r=0 then find ( beta + gamma - 3 alpha ) ( gamma + alpha - 3 beta) (alpha + beta - 3 gamma)

If alpha, beta, gamma are the roots of ax ^ (3) + bx ^ (2) + cx + d = 0 and det [[alpha, beta, gammabeta, gamma, alphagamma, alpha, beta]] = 0, alpha ! = beta! = gamma, alpha + beta-gamma, beta + gamma-alpha, and gamma + alpha-beta

If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta, gamma),(beta, gamma, alpha),(gamma, alpha, beta)|=