Question

2+6i is a zero of f(x)= x^4 - 16x^3 + 124x^2 -624x + 1440. Find the other zeros.

Answer 1

Do you know about the rational zeros theorem?

Answer 2

I assumed that another zero would be 2-6i. Then I tried multiplying (x-(2+6i))(x-(2-6i)). I eventually got x^2-4x+10. When I try to do anything else after this, I get stuck. I think I might have done something wrong.

Answer 3

Yes

Answer 4

Yeah, that is another one of the zeros,you're right. And I rethought it, the initial approach I put I think is a wrong way to go about it, I apologize xD

Answer 5

How did yoi get + 10?

Answer 6

4-6i^2

Answer 7

You need to square the 6, too.

Answer 8

I didn't realize that. That might be what is messing me up

Answer 9

maybe :p Im still working the problem myself, though.

Answer 10

Are you trying to rework the problem?

Answer 11

Yes

Answer 12

Alrighty. Let me know, I worked it out so I can help ya if youre stuck.

Answer 13

I finally found x^2-12x+36, but I forget what to do next

Answer 14

You should get x^2 -4x + 40

Answer 15

I did get that, but then I divided the whole original problem by x^2-4x+40

Answer 16

oh!! Wow, that was smart xD Smarter than what I did, haha. But yes, you did get the write remainder, x^2-12x+36, now that I look at it xD

Answer 17

** I finally found x^2-12x+36, but I forget what to do next**

you can use the quadratic formula
http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html

or you can try to factor: Look at the constant term +36 in the quadratic.
list the pair of factors that give 36
1,36
2,18
3,12
4,9
6,6

the + sign on the 36 means the two factors will have the same sign

now look at the -12x term. the minus means the larger factor is negative. Knowing that both factors have the same sign, this implies both factors are negative.

and pick out the pair of factors listed above that add to -12
(to match the -12x term)

you get (x-6)(x-6)
and the roots are x=6 and x=6
that is 6 is a repeated root of this polynomial

Answer 18

I saw that too. Thanks for the help. :)