I searched for a root finding algorithm and found QR decomposition with Companion matrix which was promising but I found a couple equations where this method didn't work.
These for example won't be solved:$$ x^4 - 10x^2 + 9, \quad x^3 - 5x^2 - 4x + 20. $$
Is it possible to modify the algorithm so that such cases can be solved? If one you reading this knows if this is possible or another algorithm that could be implemented, I hope you will be so kind and give some form of an answer.