Answer: [tex]\pm 1,\pm5,\pm7,\pm35[/tex]
Step-by-step explanation:
Given: A new company estimates its total profit as
[tex]P(x) = x^4 - 2x^3 - 240x - 35[/tex], 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)=[tex]\pm 1,\pm5,\pm7,\pm35[/tex]
By rational root theorem , we have
The rational zeros [tex]\dfrac{b}{a}=\frac{\pm 1}{ 1},\dfrac{\pm 5}{1},\dfrac{\pm7}{1},\dfrac{\pm35}{1}[/tex]
Hence, the values of x until the company breaks even = [tex]\pm 1,\pm5,\pm7,\pm35[/tex]
