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

If alpha , beta and gamma the 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) non of these

If alpha, beta, gamma are roots of equation x^(3)-x-1=0 then the value of sum(1+alpha)/(1-alpha) is :

If alpha, beta, gamma are roots of the equation x^(3) + px^(2) + qx + r = 0 , then sum (1)/(alpha beta ) =

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,beta,gamma are the roots of the equation (x^3+x^2+x+1)=0 then |{:(1+alpha^2," "1," "1),(" "1,1+beta^2," "1),(" "1," "1,1+gamma^2):}| is equal to

If alpha,beta,gamma are the roots of the equation (x^3+x^2+x+1)=0 then |{:(1+alpha," "1," "1),(" "1,1+beta," "1),(" "1," "1,1+gamma):}| is equal to

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0, then the value of (alpha-(1)/(beta gamma))(beta-(1)/(gamma alpha))(gamma-(1)/(alpha beta)) is

If alpha,beta,gamma are the roots of the equation x^(3)-px+q=0, ten find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma)

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)