# Thread: "Find all real zeros of the function"-help

1. ## "Find all real zeros of the function"-help

I am wondering if I can get some help with this. I really dont get where to start. Here is an exaple problem.
Find all real zeroes of the funciton
g(x)=x^3-4x^4-x-4

I use the ^ to show what power it is. thanks!

2. Originally Posted by Braz
I am wondering if I can get some help with this. I really dont get where to start. Here is an exaple problem.
Find all real zeroes of the funciton
g(x)=x^3-4x^4-x-4

I use the ^ to show what power it is. thanks!
$g(x) = x^3 - 4x^4 - x - 4$ doesn't actually HAVE any zeroes. All solutions are complex.

3. lol so no solution? also, how do i type powers?

4. Well when I am asked to find the zeroes of a function I always set it equal to zero first. In this particular equation you would have $0 = x^3 - 4x^4 -x-4$
I would then see if there was any method of factoring, this one does not. Perhaps you copied the question wrong because it actually does not have any real zeroes as far as I can tell.

5. Originally Posted by Braz
lol so no solution? also, how do i type powers?
If you click on the equation in my post, you can see the code I used to type it.

And no, there are no real solutions to that equations. The function does not cross the x axis in the xy plane. It has 4 complex solutions. Have you met complex numbers yet?

6. lol yes, i copied wrong its
$g(x)=x^3+4x^2-x-4$

7. Originally Posted by Braz
lol yes, i copied wrong its
$g(x)=x^3+4x^2-x-4$
well, in that case, note that

$x^3 + 4x^2 - x - 4 = x^2(x + 4) - (x + 4) = (x + 4)(x^2 - 1) = (x + 4)(x + 1)(x - 1)$

can you finish?

8. Start by factoring. Take out the $x^2$ and you get $x^2(x+4) - (x+4)$ which factors further.. but I will not do your homework lol.

9. so x=-4,1,-1 ? what does it mean by all real zeroes? is that it?

10. im not asking you to do my homework lol, just 1 problem so I can use it to help me with the rest. I am terrible at math and have a terrible teacher who has been teaching for 1 year lol. so glad i found this forum.

11. Originally Posted by Braz
so x=-4,1,-1 ? what does it mean by all real zeroes? is that it?
yes

an nth degree polynomial has n roots (up to multiplicity, and including complex ones), this is from the Fundamental Theorem of Algebra. so this is all the roots, since you had a 3rd degree polynomial

12. Originally Posted by Braz
so x=-4,1,-1 ? what does it mean by all real zeroes? is that it?
The zero is where the function equals zero or to picture it, where the graph of the function crosses the x-axis. That's how I have always thought of it. If you can use a graphing calculator, you should.

13. ok so let me try this i have $f(x)=x^3+x^2-2x-2$
then i take out the x so $x(x^2=x-4)$ where do i go from there?

14. Originally Posted by Braz
ok so let me try this i have $f(x)=x^3+x^2-2x-2$
then i take out the x so $x(x^2=x-4)$ where do i go from there?
even if you took out the x, that is not what you would get. see what i did last time in post #7, it is the same thing you must do here

15. uggh i still dont get it. please try to explain it again. i didnt get how u got the $x^2(x+4)$ thing

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