Saturday 22 April 2017

abstract algebra - Find a polynomial with roots from another

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?

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