I apologize if the title is not complete enough.
Let $f(x) = x^3 - 7x - 3$ and $g(x) = x^3 - 4x -5$ be polynomials with complex coefficients.
I need to find a polynomial of degree $3$ with roots $g(x_1)$, $g(x_2)$, and $g(x_3)$, where $x_1$, $x_2$ and $x_3$ are roots of $f$. The coefficient in front of $x^3$ must be $1$.
I can't find roots of $f$. Any suggestions?