If `alpha, beta, gamma` are the roots of the equation `x^3+ qx +r =0`then find the equation whose roots are (a) `alpha+beta, beta+gamma, gamma+alpha` (b) `alpha beta, beta gamma, gamma alpha`

If `alpha, beta, gamma` are the roots of the equation `x^3+ qx +r =0`t

1.	If `alpha, beta, gamma` are the roots of the equation `x^3+ qx +r =0`then find the equation whose roots are (a) `alpha+beta, beta+gamma, gamma+alpha` (b) `alpha beta, beta gamma, gamma alpha`
Answer» a)`alpha+beta+gamma=0` `alphabeta+betagamma+gammaalpha=q` `alphabetagamma=-r` `2(alpha+beta+gamma)=0=b` `x^3-bx^2+cx-d=0` `C=alphabeta+alphagamma+beta^2+betagamma+betaalpha+gamma^2+gammaalpha+alphabeta+alpha^2+alphabeta` `c=(alpha+beta+gamma)^2+(alphabeta+gammabeta+alphagamma)` `c=q` `d=(alpha+beta)(beta+gamma)(gamma+alpha)` `d=alphabeta+alphagamma+beta^2+betagamma)(alpha+gamma)` `d=alphabetagamma+alphagamma^2+beta^2gamma+betagamma^2+alpha^2beta+alpha^2gamma+beta^2gamma+alphabetagamma` `d=r` `x^3+2x+r=0` `b)b=alphabeta+betagamma+gammaalpha=q` `c=alphabeta^2gamma+betagammaa^2alpha+alpha^2betagamma` `=alphabetagamma(alpha+beta+gamma)=0` `d=alpha^2beta^2gamma^2=r^2` `x^3-qx^2+0x-r^2=0` `x^3-qx^2-r^2=0`.