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 and beta are the roots of 4x^2 + 3x + 7 = 0 then the value of alpha beta

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 the equatiion x^(3)-px^(2)+qx-r=0 find sumalpha^(2) beta

If alpha and beta are the roots of x^2+x+1=0 , then alpha^16 + beta^16 =

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 a n d beta are the roots of x^2-3x+2=0 find the value of (1+ alpha )(1+ beta ).

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 f(x)= ax^(2)+bx+c,a,b,c in R and eqation f(x)-x=0 has imaginary roots alpha,beta,gamma "and " delta be the roots of f(x) -x=0 then |{:(1,alpha,delta),(beta,0,alpha),(gamma,beta,1):}| is

If alpha and beta are the roots of the equations x^2-p(x+1)-c=0 , then (alpha+1)(beta+1)_ is equal to: