If , and are the roots of the equation x^3+p x^2+q x+r=0 , then the coefficient of x in the cubic equation whose roots are ( + ), ( + ) and ( + ) is

Step-by-step solution

Since, , and are the roots of f(x)=x^3+p x^2+q x+r=0 . + + =-p, + + =q and =-r Let x= ( + )= + + - satisfies the given equation. aligned f( )= ^3+p ^2+q +r & =0 r^3 (x-q)^3 + p r^2 (x-q)^2 + q r (x-q) +r & =0 (x-q)^3+q(x-q)^2+p r(x-q)+r^2 & =0 aligned Coefficient of x=3 q^2-2 q^2+r p=q^2+p r