Question

Pre-Calc - find the complex zeros of the polynomial function

x^4 - 8x^3 + 16x^2 + 8x - 17

Answer 1

\[x ^{4} - 8x ^{3} + 16x ^{2} + 8x -17\]

Answer 2

please thoroughly explain

Answer 3

@jdoe0001 help please? Thanks

Answer 4

By inspection 1 is a zero,
do the synthetic division, wat do you get for cubic polynomial ?

Answer 5

thanks, I feel really dumb right now. I kept doing 17 and -17 and I forgot that 1 is an option. I am trying that now.

Answer 6

-1 works thanks

Answer 7

:) rational root theorem says possible rational roots are : \(\pm 1, \pm 17\)
so we better try them and see if we get lucky wid atleast 1...

then synthetic division gives us a simplified cubic

Answer 8

yeah divide x+1

Answer 9

and so does 1

Answer 10

I mean that both 1 and -1 work

Answer 11

yup ! divide them one by one

Answer 12

now I have x^2 - 8x + 17

Answer 13

? sorry, I think I should know what to do next, but I don't

Answer 14

keep dividing? Or will it be a complex root?

Answer 15

factor ?

Answer 16

or simply use quadratic formula

Answer 17

or complete the square

Answer 18

quadratic is very easy to deal wid, cuz we have 3 ways to approach..

Answer 19

duh, quadratic formula (facepalm)

Answer 20

I feel really silly now :P

Answer 21

:)

Answer 22

I have to leave now, but you have been a big help! Thanks a bunch

Answer 23

np :)