Question

I will award a medal!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Using complete sentences, explain how to find the zeros of the function f(x) = 2x3 – 9x + 3.
Create your own polynomial with a degree greater than 2 and find the zeros of the function.

Answer 1

Thank you for showing up.

Answer 2

Well first you could use an online graqphing tool

Answer 3

Personally, I would type \[\text{Solve}\left[2x^3-9x+3==0,x\right]\]into my handy Mathematica window :-)

Answer 4

http://www.wolframalpha.com/input/?i=2x3%20%E2%80%93%209x%20%2B%203&t=crmtb01&f=rc

Answer 5

What is your handy mathematical window

Answer 6

It's a computer program

Answer 7

Mathematica is a math workbench if you will, built by the people who built WolframAlpha

Answer 8

OHHHHHHHHHHHHHH so I went on it and it did not give me the zeros.

Answer 9

the website i gave you? its sohuld be right below the grpah of it

Answer 10

it did, but you might not have understood it :-)

Answer 11

Probably.:)

Answer 12

it calls them roots, not zeros...

Answer 13

Oh so they are not whole numbers ?

Answer 14

for some amusement, click the "Exact forms" button

Answer 15

nope, because you could factor it easily if so

Answer 16

Ok so what do I put in as a answer or do I just leave it blank.

Answer 17

Oh, you could mumble something about using Cardano's solution for the depressed cubic, that always impresses the girls :-)

Answer 18

You can use Descartes' rule of signs to help with the possible number of real zeros, but that will be of limited help. Much more importantly, you can try all positive and negative factors of 3 over all possible factors of 2, but that will only help find rational zeros. There are some much more difficult techniques that are rarely even taught anymore variously called either Cardano or Tartaglia techniques (among others) that will give you your zeros, but the techniques are extremely complicated and beyond the high-school level. Hardly even taught in college anymore.

Answer 19

OK so my teacher is a guy and I do not want a academic integrity case.

Answer 20

This will give you a glimpse of the complexity of the techniques:

http://en.wikipedia.org/wiki/Cubic_function

Answer 21

oh, no, I mean the girls in the library who are watching you do the homework, not the teacher :-)

start trying values of x from say 0, moving in each direction by 1. so 0, 1 2, 3 4 5
notice when the sign of f(x) changes. that means there's a zero between the current value of x and the previous one.
also do that going in the negative direction along the axis.

Answer 22

Ok so I just use the dcartas rule and that is it right.

Answer 23

I do my home work at home and I am cool like that. Thnx

Answer 24

no, Descartes just tells you possible combinations of types of roots/zeros. to actually find zeros, you need either heavy-duty math, or an iterative numeric solver, or use my approach of trying sample values...

Answer 25

Descartes will only tell you if there is exactly one negative or exactly one positive real root. Say there is one positive real root. You could have zero or two negative real roots.

Answer 26

Ok so I get both of your explanations but after that what do I do for the second question.

Answer 27

You can work backwards with:

y = (x - a)(x - b)(x - c)

Pick your a, b, and c values and make your polynomial.

Answer 28

I loathe Descartes' rule and hate it even more when I get x^5-4x^3+8x^2-6x-2 and (3-i) is a root and they say to factor the whole thing -__-

Answer 29

Ok say I pick a= 2,b=4,c=6 now can I get help finding the zeros.

Answer 30

If you select your a, b, and c, make your polynomial, you can demonstrate the solving by synthetic division. That's what I would do.

ok, y= (x - 2)(x - 4)(x - 6)

Now, multiply out.

Answer 31

your roots are the numbers you pick they are the factor of the polynomial, where the graph touches zero

Answer 32

y = (x^2 - 6x + 8)(x - 6)

y = x^3 - 12x^2 + 44x - 48

Answer 33

Ok so routs are the location where the graph touches zero. Also @tcarroll010 I was getting to the equation and it resulted in y=x^3 + 32x -48

Answer 34

Now, you can solve this by synthetic division and you will get your roots. You know it will work, because you "pre-selected" them.

Answer 35

But why divide if I already know it is right and also if I am only asked for the roots.

Answer 36

Well, you would either use synthetic division or long division because your part b asks you to show how to solve it.

Answer 37

Oh yeah true you just gotta show ok this is how I made it, and this i s how i break it down

Answer 38

No you missed up the first question and the second the second only asks for the equation and the roots the first one asks for the explanation.

Answer 39

You see, the part about pre-picking your zeros is not part of what you show others. It is just to come up with something you know is solvable. You don't want to arbitrarily pick coefficients and come up with some impossibly-hard cubic that requires Tartaglia or Cardano.

Answer 40

Your part b, where there is a sentence starting out with "create your own" asks you to solve it. So you want to pick good coefficients, which means you better work backwards like I outlined.

Answer 41

Ok that is one part and for the roots what do I do.

Answer 42

As for your first question, my first several posts were aimed solely at that particular question.

Answer 43

no I mean the roots for the second question sorry if I am giving you a hard time.

Answer 44

That is described in my post which starts out: "If you select . . ." that post and the one after it.

Answer 45

Ok so my roots are 2,4,6 am I correct or not?

Answer 46

Yes, those are the roots I used to build you your cubic polynomial.

Answer 47

Why thank you so very much I really appreciate your help and the others and your kind patience. THANK YOU A+++++++++++++ HELP REALY FIND YOU TERRIFIC AT EXPLAINING AND YOU ARE A OCEAN OF KNOWLEDGE

Answer 48

You are very appreciative! You're great to work with!