Question

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.

1 - 2i is a zero of f(x) = x^4 - 2x^3 + 6x^2 - 2x + 5.

Answer 1

i think all complex numbers come in pairs of conjugates

Answer 2

check if (1+2i) is a zero by plugging it into the equation

Answer 3

yes it's a zero so doesn't that mean 1-2i is a zero too?

Answer 4

well, if i read that right; 1-2i is already given as a zero; and since complex numbers come in pairs of conjugates; 1+2i would be a zero as well by some forgotten thrm ....

Answer 5

yeah that's what I meant :) but I'm not sure how to plug it in

Answer 6

the complex conjugate root theorem (-: Just because I am curious, do you need to find ALL solutions? Because that seems a bit sadistic to me

Answer 7

oh, I just read "one other" I guess that means only one more.

Answer 8

if that ccr thrm is good, then your explanation just needs to say; by the ccr thrm, yada yada is a zero

Answer 9

x^4 -2x^3 +6x^2 -2x +5
0 1+2i -5 1+2i -5
--------------------------
1+2i ) 1 -1+2i 1 -1+2i 0


it pans out using synthetic division as well

Answer 10

oh okay what is the ccr theorem?

Answer 11

http://bit.ly/OjvJHE

Answer 12

so would I say
(1+2i)(1-2i)= 1 -1+2i + 1 -1 +2i ?

Answer 13

no

Answer 14

(1+2i)(1-2i) = 5 ....

Answer 15

without knowing the content of your material; and the manner in which you get graded; its going to be a shot in the dark as to what consititutes a suitable response