We have two numbers $\alpha$ and $\beta$.
We know that $\alpha$ is root of polynomial $P_n(x)$ of degree $n$ and $\beta$ is root of polynomial $Q_m(x)$ of degree $m$.
How do you find polynomial $R_{n m}(x)$ which has root equal to $\alpha+\beta$ without finding values of roots?
All polynomials are with integer coefficients.
One more question, can it be found using matrix determinant?