Question

How do you find the real zeros for f(x)=x^3-3x^2+8 ?

Answer 1

@Hero do you think you can help me with this problem?

Answer 2

Yes, for this you start with x = 1. If f(1) = 0 then you have found 1 of the zeroes. If not proceed to x = 2. keep going until you find a value for x such that f(x) = 0.

Answer 3

use only the factors of that constant term, 8.
so do what Hero says using -8, -4, -2, -1, 1, 2, 4, 8

Answer 4

hmmm... what class is this for?

Answer 5

Honors algebra2 and I'm still confused like I don't understand how to solve this

Answer 6

ok... seems the procedure we mentioned won't work unless the function is factorable.
this function is NOT factorable: f(x)=x^3-3x^2+8.

is the function correctly written?

Answer 7

yes, I wrote it correctly.

Answer 8

ok...
since this is a third degree polynomial, the only other way to i can think of is using a graphing calculator...
are you allowed to use it?

Answer 9

No my unfortunately my teacher doesn't let us. When it's asking for the real zeros is it asking for the x's?

Answer 10

yes.. it's asking for the x-intercepts....
and they are not "nice" values...

Answer 11

@ByteMe don't panic

Answer 12

Oh okay and I'm really not good with 3rd degrees factoring them is difficult for me maybe you guys could help me?

Answer 13

I would have learned a way to do it, but someone else scammed out on me.

Answer 14

I'm pretty sure to solve this, you'll need a calculator.

Answer 15

I guess since this isn't a test or quiz I can use a calculator on hw, but I wouldn't know what to do if I saw this on a test.

Answer 16

If you had to solve this on a test you would have to figure it out manually by plotting points strategically. for example

f(0) = 8
f(1) = 6
f(2) = 10

etc...
But just doing that, I'm starting to see a patten

Answer 17

Well I looked it up also and it say I can use rational root theorem I'm going to try and apply that, hopefully I can

Answer 18

Oh okay so you guys where right then I need to do synthetic division to see if each of those values of p/q can be a zero!

Answer 19

since it is not factorable, even synthetic division will not work...

Answer 20

how can you tell if it's factorable?

Answer 21

if the problem was meant to be solved using synthetic division, rational root theorem, factoring, it would have been factorable.

Answer 22

how can i tell if it's factorable? i used synthetic division with the numbers i stated in my first post.

Answer 23

Okay so is my answer, no solution?

Answer 24

and as you can see, even wolfram alpha agrees..
http://www.wolframalpha.com/input/?i=factor+x%5E3-3x%5E2%2B8

Answer 25

there IS a solution...

Answer 26

as you can see, the root is not nice...
http://www.wolframalpha.com/input/?i=solve+x%5E3-3x%5E2%2B8%3D0

Answer 27

Okay thank you this helps!

Answer 28

and btw, the roots of this function are 1 real and 2 complex. those are the nature of your roots.

Answer 29

you're welcome...:)
use wolfram... it really helps...

Answer 30

yeah it does thanks for the resource :)

Answer 31

:)

Answer 32

good luck to you...

Answer 33

I knew all along there was something wrong with this one.

Answer 34

@Hero thank you for your help too! lol yeah this was a complicated problem, but I appreciate the help you guys!!

Answer 35

Make sure you come back with your teacher's solution. Apparently he or she can do it without the calculator.

Answer 36

haha yeah I'll ask her how she does it w/o a calculator. She was on vacation for a week when we learned this and the sub kept telling us to use a calculator which didn't help and then the week after that I got the flu so I'm kind of behind and slowly catching up. I'm so happy I found open study!