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

once again we can find the polynomial with those zeros, pretty much in our heads now right?

Answer 2

it is
\[x^2-2x+5\]

Answer 3

yes

Answer 4

your next job is to either divide or factor

Answer 5

\[x^4 - 2x^3 + 6x^2 - 2x + 5=(x^2-2x+5)(quadratic)\]

Answer 6

you can do it by division, or by thinking
thinking is easier, because long division sucks

Answer 7

plus, there is no good way to write long division here
want to use the think method?

Answer 8

So what exactly I am dividing is where Im at

Answer 9

did you understand up to here \[x^4 - 2x^3 + 6x^2 - 2x + 5=(x^2-2x+5)(quadratic)\]
?

Answer 10

Yes that (x^2 +1)(x^2 -2x +5) equals x^4 - 2x^3 + 6x^2 - 2x + 5

Answer 11

oooh
ok then you are done

Answer 12

But then what is the zero ?

Answer 13

actually the way i read the problem, it is actually much much easier than even that

Answer 14

hmm?

Answer 15

"Using the given zero, find one other zero of f(x)"

Answer 16

Would I plug that in for x?

Answer 17

since \(1-2i\) is a zero, the other zero must be its conjugate \(1+2i\)
done
finished
easy

Answer 18

that is all it is asking for
one zero is \(1-2i\) find another one
all that work for nothing

Answer 19

wooowwwwwwww if I would have thought of that a million years ago haha thanks again!!!!

Answer 20

btw once you did all that work, you have all the zeros
\(1+2i,1-2i\) and from \(x^2+1\) you get \(i\) and \(-i\)
not that it asked ...

Answer 21

yw

Answer 22

Oh okay thanks aton haha I gtg to bed now its 11:35 o.o !