0=x^4 + 2x^3 + 6x^2 - 3x - 7
What is x?

Question

0=x^4 + 2x^3 + 6x^2 - 3x - 7
What is x?

ganeshie8 · Answer

familiar with below goodies ?
1) rational root theorem
2) synthetic division

anonymous · Answer

yes

ganeshie8 · Answer

nvm, they're not going to work :/

anonymous · Answer

I tested it with 1, but its just over 1

ganeshie8 · Answer

can you double check the equation please ?

ganeshie8 · Answer

just to make sure there are no typoes..

anonymous · Answer

Here, I directly copied and pasted
P(x) = x4 + 2x3 + 6x2 - 3x - 7

 think it is the same...

anonymous · Answer

only added the "^" because they were exponents

ganeshie8 · Answer

yeah, im not sure how to solve this algebraically (although there is a direct formula to solve a quartic polnomial equation) 
are you given any instructions on the method to be used ?

anonymous · Answer

This is all I have 
You are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function P(x) = x4 + 2x3 + 6x2 - 3x - 7. Describe to the CEO what the graph looks like. Use complete sentences and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0)


Did I set it up wrong?

anonymous · Answer

I zoomed in on a graph and it said about 1.05

ganeshie8 · Answer

Alright, so there are two parts to this question :
1) end behaviors of the graph and 
2) where the company will break even (where P(x) = 0)

ganeshie8 · Answer

what did you put for part 1 ?

anonymous · Answer

At first, the graph will be very negative. Not much profit will be made. But as more and more soda is produced and sold, the line begin to come back up, and the larger the x becomes, the larger the y becomes

ganeshie8 · Answer

that looks good, you may also want to explain something about relation between endbehavior and degree/leading coefficient.

anonymous · Answer

What do you mean?

ganeshie8 · Answer

What does the degree of a polynomial tell you about the end behavior ?

anonymous · Answer

It will be positive?

ganeshie8 · Answer

degree = highest exponent 

$ \large P(x) = x^{\color{red}{4}} + 2x^3 + 6x^2 - 3x - 7$

anonymous · Answer

Right, but does that mean that the graph will have a positive outcome?

ganeshie8 · Answer

Since the degree of $P(x)$ is 4, which is even, the graph goes in SAME directions on  left and right extremes.

anonymous · Answer

So it will always be like a u,  not an s?

ganeshie8 · Answer

|dw:1404090946258:dw|

ganeshie8 · Answer

Exactly ! it will be always like an U or an inverted U, but never a S

ganeshie8 · Answer

It could be like an inverted U also - depends on the sign of leading term

ganeshie8 · Answer

Look at the given polynomial once again, whats the sign of leading coefficient ? is it positive or negative ?

anonymous · Answer

positive, so its a regular u

ganeshie8 · Answer

Yep ! append all that we discussed to your essay... that should conclude part 1.

ganeshie8 · Answer

lets look at part 2

ganeshie8 · Answer

2) where the company will break even (where P(x) = 0)

anonymous · Answer

When I zoomed in on a graph of it, it crossed at about (1.05,0)

anonymous · Answer

I set that equation equal to 0 and thats about what I got

ganeshie8 · Answer

Yes, thats a valid breakeven point; just explain in your own words how you found that zero and why it is called a breakeven point etc..

anonymous · Answer

So would I just say that I made a table? How could I prove it?

ganeshie8 · Answer

tbh, im not really sure - I can see why you're hesitating to say that you have used graphing technology... cos the essay is about sketching, so graphing is strictly not allowed here.

anonymous · Answer

Hmmmmm Okay, Thank you so much! I'll figure it out!

ganeshie8 · Answer

good luck !