Question 1160754
Check that (2+i) is a root of z^4+2(z^3)-9(z^2)-10z+50=0. Find the remaining three roots.
<pre>{{{matrix(1,3, z^4 + 2z^3 - 9z^2 - 10z + 50, "=", 0)}}}
As 1 root is 2 + i, its conjugate/other root is: 2 - i
With  2 + i and 2 - i being roots, we get: z = 2 + i and z = 2 - i, and so, FACTORS are: z - 2 - i and z - 2 + i.
The above expands to {{{matrix(1,7, (z - 2)^2 - i^2, "====>", z^2 - 4z + 4 - - 1, "====>", z^2 - 4z + 4 + 1, "====>", z^2 - 4z + 5)}}}
Using synthetic division or long division of polynomials, we find that the quotient is: {{{z^2 + 6z + 10}}}.
Now, since this quotient CANNOT be factored, you can use the quadratic equation formula, or "complete the square" to find the other 2 roots.