You can
put this solution on YOUR website!
write an equation that has a root of 3+i.
If it is to have real coefficients, then if one of its
roots is 3+1, it must have 3-i as another root. We can
make an equation with just those two roots:
If we were solving it and ended up with
x = 3 + i and x = 3 - i
Then to get that we would have had to set two expressions = 0
using the zero factor principle. So before that we would have
had:
x - 3 - i = 0 and x - 3 + i = 0
Then before that we must have had
(x - 3 - i)(x - 3 + i) = 0
And before that we must have had
x² - 3x + ix - 3x + 9 - 3i - ix + 3i - i² = 0
Collecting terms:
x² - 6x + 9 - i² = 0
Replacing i² by -1
x² - 6x + 9 - (-1) = 0
x² - 6x + 9 + 1 = 0
x² - 6x + 10 = 0
That's it.
Edwin
