if `alpha,beta,gamma `are the roots of `x^3-3x^2 +3x + 7 =0` then `(alpha-1)/(beta-1)+(beta-1)/(gamma-1)+(gamma-1)/(alpha-1)`

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

If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 The value of |{:(alpha, beta ,gamma),(gamma,alpha ,beta),(beta,gamma ,alpha):}| is equal to

If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 . If a = alpha^(2)+beta^(2)+gamma^(2),b= alphabeta+betagamma+gammaalpha the value of |{:(a,b,b),(b,a,b),(b,b,a):}| is

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)

If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 . If the absolute value of the expression (alpha-1)/(alpha+2)+(beta-1)/(beta+2)+(gamma-1)/(gamma+2) can be expressed as (m)/(n) where m and n are co-prime the value of |{:(m,n^(2)),(m-n,m+n):}| is

If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^2+7x-9=0, then the value of (1+alpha^2)(1+beta^2)(1+gamma^2)(1+sigma^2) is a. 9 b. 11 c. 13 d. 5

Let alpha,beta,gamma be the roots of (x-a) (x-b) (x-c) = d, d != 0 , then the roots of the equation (x-alpha)(x-beta)(x-gamma) + d =0 are :

Answer each question by selecting the proper alternative from those given below each question so as to make the statement true : If alpha, beta" and "gamma are the zeroes of the cubic polynomial ax^(3)+bx^(2)+cx+d , then (1)/(alpha)+(1)/(beta)+(1)/(gamma)="............."

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

If alpha,beta,gamma are the cube roots of p, then for any x,y,z (x alpha + y beta + z gamma)/(x beta + y gamma + z alpha =