Question

A new company estimates its total profit (profit = total revenue minus total cost) as P(x) = x4 – 2x3 – 240x – 35, where P is in hundreds of dollars and x is the number of months elapsed since the company’s start-up. According to the rational zero theorem, what can be the values of x until the company breaks even?

Answer 1

With ruffini you easily get 5.6666 months

Answer 2

Answer: $\pm 1,\pm5,\pm7,\pm35$

Step-by-step explanation:

Given: A new company estimates its total profit as

$P(x) = x^4 - 2x^3 - 240x - 35$, where P is in hundreds of dollars and x is the number of months elapsed since the company’s start-up.

The coefficient of the leading term (a)= 1

The constant term = 35

The factors of 35 (b)=$\pm 1,\pm5,\pm7,\pm35$

By rational root theorem , we have

The rational zeros $\dfrac{b}{a}=\frac{\pm 1}{ 1},\dfrac{\pm 5}{1},\dfrac{\pm7}{1},\dfrac{\pm35}{1}$

Hence, the values of x until the company breaks even = $\pm 1,\pm5,\pm7,\pm35$