The fundamental theorem of algebra

Find the roots of the polynomial $p(z)=z^{2}-6z+13$.

Find the roots of $p(z)=z^{3}+5z^{2}+4z-10$. Hint: one of the roots is $z=1$.

Factor $z^{3}-3z+2$ into a product of linear factors.

Let $p(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots+a_{1}x+a_{0}$ be a polynomial with real coefficients, i.e., such that all the $a_{k}$ are real numbers. Suppose that $z$ is a root of $p$. Show that $\overline{z}$ is also a root of $p$.