Question

a certain company’s main source of income is a mobile app.
the company’s annual profit (in millions of dollars) as a function of the
app’s price (in dollars) is modeled by
p(x) = -2(x - 3)(x - 11)
which app prices will result in $0 annual profit?
enter the lower price first.
lower price: dollars
higher price: dollars
related content
quadratic word problems (factored form)

Explanation:

Step1: Set profit function to 0

We want to find \( x \) when \( P(x) = 0 \). So we set the equation \( -2(x - 3)(x - 11)=0 \).

Step2: Solve for x using zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both). In our equation, we can divide both sides by - 2 (since \(-2
eq0\)) to get \((x - 3)(x - 11)=0\).
Now, applying the zero - product property:

• Case 1: \( x - 3=0 \), then \( x=3 \).
• Case 2: \( x - 11=0 \), then \( x = 11 \).

Answer:

Lower price: 3 dollars
Higher price: 11 dollars