If `alpha, beta, gamma` are roots of the equation `x^(3)+px^(2)+qx+r= 0`, then prove that `(1-alpha^(2))(1- beta^(2)) (1- gamma^(2))=(1+q)^(2)-(p+r)^(2)`

If alpha and beta are the roots of the equation x ^(2) + alpha x + beta = 0, then

If alpha and beta are the roots of the equation x^(2)-7x+1=0 , then the value of 1/(alpha-7)^(2)+1/(beta-7)^(2) is :

If alpha, beta, gamma are the roots of the equation x^(3)+4x+1=0 , then find the value of (alpha+beta)^(-1) +(beta +gamma)^(-1) + (gamma+ alpha)^(-1)

If alpha and beta are the roots of the equation x ^(2) + 3x - 4 = 0 , then (1)/(alpha ) + (1)/(beta) is equal to

If alpha,beta,gamma are roots of the equation x^(2) (px+q)=r(x+1), then the value of determinant |(1+alpha,1,1),(1,1+beta,1),(1,1,1+gamma)| is a) alpha beta gamma b) 1+(1)/(alpha)+(1)/(beta)+(1)/(gamma) c)0 d)None of these