Question

HELP ASAP PLEASE Question:

Answer 1

@explorerhills @sweetburger

Answer 2

@Photon336

Answer 3

@sweetburger

Answer 4

please help!!

Answer 5

Wait so all three of those have to be roots?

Answer 6

@nincompoop

Answer 7

Remember the conjugate zeroes theorem? If a+bi is a zero, then a-bi is also a zero.

So they gave you 8, -14, and 3 + 9i... but there's one more, what is it?

Answer 8

Once you realize that fourth zero, just plug all the zeroes in like so: \[\large (x- [zero])(x- [zero])(x- [zero])(x- [zero])\]replacing the [zero] with the given zeroes, and simplify.

Answer 9

so how would I get my answer though

Answer 10

can you just tell me the steps please, I am writing a study guide and need a solid example:-)

Answer 11

(this one^) please

Answer 12

@agent0smith

Answer 13

Go back and answer my question, first.

Answer 14

@agent0smith the other 0 is 2

Answer 15

No it isn't.

Remember the conjugate zeroes theorem? If a+bi is a zero, then a-bi is also a zero.

So they gave you 8, -14, and 3 + 9i... but there's one more, what is it?


Eg. if a zero was 3-5i, another zero must be 3+5i.

Answer 16

so the other is 3-9i

Answer 17

Yes.

Answer 18

so what would i do next

Answer 19

I gave the next step already.

Answer 20

and then thats it once i do that?

Answer 21

or not distribute, factor out

Answer 22

@agent0smith

Answer 23

That's the long hard part, so far you've only done the easy part

(x-8)(x+14)(x-3+9i)(x-3-9i)

Start by expanding the (x-8)(x+14)

Then expand the (x-3+9i)(x-3-9i)

Answer 24

x^4 - 11x^3 + 72x^2 - 606x + 10,080

Answer 25

Idk maybe. I assume you just plugged that into wolfram or something.

Answer 26

ok

Answer 27

thanks you're a big help. Lol i did it and thats what I got!! sheesh

Answer 28

never mind its not right, i redid it and its the last one. Thanks fort the help

Answer 29

idk what the options are but scroll down to see the correct expression here https://www.wolframalpha.com/input/?i=(x-8)(x%2B14)(x-3%2B9i)(x-3-9i)

Answer 30

An easy way to expand the pesky ones (z' is conjugate of z):

\[(x - z)( x - z') = x^2 - xz'-xz +zz' =x^2 -x(z+z')+zz' \]
\[= x^2 - 2 \mathbb{R}e(z) x +|z|^2\]