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

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

Bytelearn · Accepted Answer

Set Equation Equal to Zero: To find the app prices that result in $0 annual profit, we need to solve the equation P(x) = -2(x-3)(x-11) = 0.Simplify Equation: Set the profit function equal to zero and solve for x: -2(x-3)(x-11) = 0.Apply Zero Product Property: Divide both sides of the equation by -2 to simplify: (x-3)(x-11) = 0.Solve for x (1st Factor): Apply the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, set each factor equal to zero: x-3 = 0 or x-11 = 0.Solve for x (2nd Factor): Solve the first equation for x: x-3 = 0, so x = 3.Identify App Prices: Solve the second equation for x: x-11 = 0, so x = 11.The two app prices that result in $0 annual profit are $3 and $11. Since we need to enter the lower price first, the lower price is $3 and the higher price is $11.

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