Question

An entrepreneur estimates that the total profit from his proposed company will be given by the foundation p(x)=x^3-4x^2+3x-12 where p is in hundreds dollars and x is the number of years elapsed after the company starts operation. in how many years will the company break even?

Answer 1

Set p(x) = 0 and solve for x.

x^3 - 4x^2 + 3x - 12 = 0
x^3 - 4x^2 ... + 3x - 12 = 0, cut in half and factor
x^2 (x-4) ... +3 (x-4) = 0, regroup
(x^2 + 3) (x-4) = 0, set each part equal to zero and solve

x^2 + 3 = 0, subtract 3 from both sides
x^2 = -3, take square root of both sides
x = sqrt (-3) which is imaginary.

x-4 = 0, add 4 to both sides
x = 4

Since we do not want complex/imaginary numbers involved, our answer is 4. They will break even in 4 years.