Recover a quartic and reuse its real roots for intersections

A graphing calculator is not to be used in answering this question.

One root of $x^4+ax^3+5x^2-x-10=0$, where $a$ is real, is $x=1+2i$. Find $a$ and the other roots.5 marks

Hence find the $x$-coordinates of the intersection point(s) of $y=5(x^2-2x^4)$ and $y=x^3+3x-1$.3 marks