Problem

Source: Canada Repêchage 2019/3 CMOQR

Tags: polynomial, algebra, roots



Let $f(x) = x^3 + 3x^2 - 1$ have roots $a,b,c$. (a) Find the value of $a^3 + b^3 + c^3$ (b) Find all possible values of $a^2b + b^2c + c^2a$