Answer:
The possible values of x until the company breaks even are [tex]\pm 1,5,7,35[/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.
To find : According to the rational zero theorem, what can be the values of x until the company breaks even?
Solution :
Applying ration zero theorem,
The constant term is 35
Factors of 35 is [tex]p=\pm 1,5,7,35[/tex]
The leading coefficient is 1
Factors of 1 is [tex]p=\pm 1[/tex]
Rational zeros are [tex]\frac{p}{q}=\frac{\pm 1,5,7,35}{\pm 1}[/tex]
i.e, The rational zeros are [tex]\pm 1,5,7,35[/tex]
Therefore, The possible values of x until the company breaks even are [tex]\pm 1,5,7,35[/tex]
