Select all the correct answers

A bicycle manufacturer uses the given expression to model the monthly profit from sales of a new model of bicycle, where x is the selling price

of one bicycle, in dollars.

-x^2+300x-20,000

At what selling prices for the bicycle will the manufacturer make neither a profit nor a loss?

$50

$300

$100

$200

$250

$150

The correct answers are C. $ 100 and D. $ 200.

Step-by-step explanation:

Let's solve for x the profit from sales equation, this way:

-x^2 + 300x - 20,000 = 0

x = selling price of one bicycle, in dollars.

The information given tells us that we should calculate the selling prices (x) to make neither a profit nor a loss, in other words, $ 0.

-x² + 300x - 20,000 = 0

x² - 300x + 20,000 = 0 (Multiplying by - 1 at both sides)

Factoring, we have that:

- 200 + - 100 = - 200 - 100 = - 300

-200 * - 100 = 20,000

Therefore,

(x - 200) * (x - 100) = 0

x₁ = x - 200 = 0 ⇒ x = 200

x₂ = x - 100 = 0 ⇒ x = 100

The correct answers are C. $ 100 and D. $ 200.