A bike manufacturer can predict profits, P, from a new sports bike using the quadratic function P (x) = - 100x2 + 46,000x - 2,100,000, where x is the price of the bike. At what prices will the company make $0 in profit?

At $51.39 and $408.61, the company will make $0 in profit.

Step-by-step explanation:

Hi there!

Let's write the function:

P (x) = - 100 x² + 46,000 x - 2,100,000

We have to find the value of x at which P (x) = 0:

0 = - 100 x² + 46,000 x - 2,100,000

Using the quadratic formula, we can solve this quadratic equation:

a = - 100

b = 46,000

c = - 2,100,000

x = [-b ±√ (b² - 4ac) ]/2a

x = [-46,000 ± √ (46,000² - 4 (-100) (-2,100,000) ] / 2 (-100)

x = (-46,000 ± 35,721.14) / -200

x₁ = (-46,000 + 35,721.14) / -200

x₁ = 51.39

x₂ = (-46,000 - 35,721.14) / -200

x₂ = 408.61

Then at $51.39 and $408.61 the company will make $0 in profit.