Algebra question

Question

The profit formula for a small business is p = −x² + 160x − 6000.

 Find the set of x-values that will keep the profit positive. (Enter your answer using interval notation.)

Answer 1

Could also multiply both sides by -1

x² - 160x + 6000 = 0 and factor: (6000 is 100 x 60, not too difficult to find)

(x - 100)(x - 60) = 0

x = 100; x = 60 ,etc.

Answer 2

First, you'll want to find the roots of the equation using the quadratic formula:

x = (-b ± √(b² – 4ac)) / 2a

In your equation:

a = -1

b = 160

c = -6000

Therefore, the roots are:

x = 80 ± 20

so

x = 60 and x = 100

Those roots are the breakeven points for the profit. Therefore, the set of x-values that will keep the profit positive (using interval notation) are written as:

x = (60, 100)