f(x)=x^4-3x^3+6x^2-2x-12
find real zeros

- anonymous

f(x)=x^4-3x^3+6x^2-2x-12
find real zeros

- katieb

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- anonymous

can you factor that expression?

- anonymous

I've tried to... but I can't figure it out.

- anonymous

Wolfram presents the following.

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- anonymous

This makes me think there is not way to factor this. Wolfram is really good at factoring. Do you need the answer or spep by step procedure?

- anonymous

x1 -> 1.15181 - 2.23019 i
x2 -> 1.15181 + 2.23019 I
x3 -> -1.07514
x4 -> 1.77152
this are the four solutions for that expresion

- anonymous

Ok. Thanks.

- anonymous

I tried factoring, but I cant figure it out either. Lets supposse there is not a way jaja

- anonymous

there probably isnt.
Thanks for trying though! :)

- anonymous

np

- dumbcow

emunrrad how did you get your solution?
i took derivative and used newtons method and found
x = -1,2
only 2 real solutions because no inflection points exist

- anonymous

I used Mathematica from wolfram. Can you show us how to do that?

- dumbcow

using these solutions you can use synthetic division to get factored form
=(x+1)(x-2)(x^2-2x+6)

- anonymous

I tried synthetic division. But I got stoke and didn't know how to continue and just assumed I was doing it wrong.

- dumbcow

http://en.wikipedia.org/wiki/Newton%27s_method

- anonymous

gonna check it out.

- dumbcow

well to solve just by using synthetic division, there are many possibilities
any factor of -12 could work
you would have to try +-1,2,3,4,6,12
-1 and 2 should have worked for you

- dumbcow

the other 2 complex solutions would be: 1+- sqrt(5)i
from quadratic formula
x^2-2x+6 =0

- anonymous

That makes a bit more since now. Thank you.

- anonymous

Yeah, I worked it out by synthetic divsion, -1 works, then 2 works. So (x+1)(x-2)(x^2-2x+6). I hadn't done synthetic division in a while so I brushed up on it in five minutes here http://www.purplemath.com/modules/synthdiv.htm

- dumbcow

synthetic division is nice but its a lot of work for finding zeroes, especially when constant has many factors and what if none of them work, you are assuming it has integer zeroes

- anonymous

For a pre-calculus course, synthetic division would be was is expected. The heavy armo, Newton's method is for higher math, I think brokenangel is working her way there.

- dumbcow

oh sorry, yeah i agree i was just speaking in general
thats true newton method is meaningless if you haven't had calculus :)

- anonymous

haha nope. this is algebra 2 stuff for me.

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