Question

A company estimates its total profit (profit = total revenue minus total cost) as
P(x) = 2x^5 − 3x^4 − 5x^2 − 2, where P is in thousands of dollars and x is the number of years elapsed since the company was founded. How many times can the total profit become exactly zero? Hint: Use Descartes's rule of signs.

Answer 1

2 or 0



5 or 3 or 1



3 or 1



1

Answer 2

@Michele_Laino @posingocean

Answer 3

@Nnesha

Answer 4

we have to find the roots of the polynomial P(x)

Answer 5

Okay, let me do that real quick.

Answer 6

About 2.1?

Answer 7

I'm computing...

Answer 8

I got this computation:
if we set x=2, we have:
P(2)=-6 <0
whereas, if we set x=3, we get:
P(3)=176, please check those numbers
Now, since every polynomial is a continuous function, then our polynomial assumes all values between -6 and 176, so it will assume the value 0, then will exist a x-coordinate, say x_0, between 2, and 3, such that P(x_0)=0

Answer 9

Oh.. well I just Mathway and the root is x=2.111219. But if I do the rational root test then I get + or - 1, + or - 0.5 and + or - 2

Answer 10

please look at this drawing:

Answer 11

Okay, I did... I'm sorry I still don't really understand what I'm supposed to find.

Answer 12

I think that the total profit P(x) is equal to zero exactly only one time, between, say the second year and the third year

Answer 13

Oh, okay. But the options don't have a 2-3. The options are posted in the comments.

Answer 14

I think the last one, namely 1

Answer 15

That's what I was thinking too. Thank you :)

Answer 16

Thank you! :)