Question

Determine the zeros of f(x) = x4 - x3 + 7x2 - 9x - 18.

Answer 1

-1 fits in.

Answer 2

Got it, break 7 as 9-2 /

Answer 3

so \[\pm 1\] is the answer?

Answer 4

nopes.

Answer 5

What do get after writing 7 as 9-2 ?

Answer 6

\[x^4 - x^3 + 9 - 2x^2 - 9x -18\] ?

Answer 7

x^4 - x^3 + 9x^2 -2x^2 - 9x - 18.=0

=>(x^4 + 9x^2) - (x^3 -9x) -(2x^2 -18) =0

You see what should be the next step ?

Answer 8

yeah, factor each binomial, right?

Answer 9

yep.

Answer 10

(x^2 + 1) (x^2 + 9) for the first one?

Answer 11

try again.

Answer 12

I'm confused

Answer 13

x1 = 2
x2 = -1
x3 = 0 + 3i
x4 = 0 - 3i

Answer 14

So, substitute (0 - 3i) and -1 for x^2, making it ((0 - 3i) + 9(-1))?

Answer 15

so, then it would become (-3i - 9)

Answer 16

hint : divide f(x) to x^2+9
you would find your answer!

Answer 17

So, divide x^4 - x^3 + 7x^2 - 9x - 18 by x^2 + 9 ?

Answer 18

so it would be x^2 - x + 7 - x - 2 ?

Answer 19

combine like terms, and it would be x^2 - 2x + 5 , right?

Answer 20

Hmm.. Looks like you have 2 real zeros and 2 imaginary.

Answer 21

Do you still need help?

Answer 22

yes, I don't know what to do next

Answer 23

I got it! Thanks!