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

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

If alpha, beta are the roots of the equation ax ^(2) + bx + c =0, then the value of (1)/( a alpha + b) + (1)/( a beta + b) equals to : a) (ac)/(b) b) 1 c) (ab)/(c) d) (b)/(ac)

If alpha, beta are the roots of x^(2)-a(x-1)+b=0 , then find the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b)

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,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

If f(x) = a + bx + cx^(2) and alpha, beta, gamma are roots of the equation x^(3) = 1 , then |(a,b,c),(b,c,a),(c,a,b)| is equal to a) f(alpha) + f(beta) + f(gamma) b) f(alpha)f(beta) + f(beta)f(gamma) + f(gamma)f(alpha) c) f(alpha)f(beta)f(gamma) d) -f(alpha)f(beta)f(gamma)