Question

How do you find the all zeros of the equation below, both real and complex?

x^4-9x^3+2x^2-17x+94

This is for a project, I have to have it finished by tomorrow! Help?!

Answer 1

do you know how to do synthetic division?

Answer 2

Yeah

Answer 3

But what would I divide it by?

Answer 4

ok how about p/q? What numbers could be possible zeros? name some

Answer 5

http://www.wolframalpha.com/input/?i=solve+x%5E4-9x%5E3%2B2x%5E2-17x%2B94

Answer 6

I don't know what p/q is...and using the online graph won't really work, because I have to show my work

Answer 7

2 real and 2 complex solutions. Those are horrible solutions. Such a shame, they are not whole numbers. It would have been an easier problem to explain for a project.

Answer 8

Yes, but the graph supports your solution. It crosses the x axis in 2 places, so it verifies 2 real solutions, the remaining solutions are complex

Answer 9

But how do I get there? That's my problem. My teach didn't really go over it..

Answer 10

I wonder if your teacher did not realize how awful those solutions look. Are you high school level? Just curious because you probably only know how to solve for the solution by factoring or synthetic division. I am not sure you have enough math knowledge to do it by hand. This could be a technology related problem.

Answer 11

Go talk to your teacher and find out what methods they expected you to use.

Answer 12

Well we wrote the equation based on a birthday from a famous/historical person (silly I know) but the graph looked really good for what we were doing. Oh well..just my luck I get a hard one!

Answer 13

I still think the only way you can answer it is based on the graphical approach and/or using your calculator. I would do it using that approach. Make sure to state that the 4th power means you are looking for 4 solutions. Also, that complex solutions come in pairs. Good luck :)

Answer 14

Thank you!

Answer 15

anytime :)

Answer 16

When I divided I got x^3-6.86486x^2-12.65743718x-44.02540042

Do you know what to do after that? The quadratic formula is only a, b, and c, but this has a d

Answer 17

you can only use the quadratic formula for the second power. Your polynomial is the 4th power. You can't use the quadratic formula. sorry

Answer 18

I figured, so what would I do?

Answer 19

You have to use synthetic division but p/q doesn't help with any zeros.
We have a theorem called p/q and you take the factors of it to determine possible zeros.
I have checked and I do not believe there is much you can do without the graph or graphing calculator.

Answer 20

Okay, thanks