An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function p(x) = x3 – 4x2 + 3x – 12, where p is in hundreds of dollars and x is the number of years elapsed after the company starts operations. in how many years (x) will the company break even (no profit, no loss)?

To determine the number of years when the company will breakeven, we use the equation given. At the breakeven point, the company has no profit and loses. So, we P(x) = 0. We calculate as follows:
P(x) = x3 – 4x2 + 3x – 12
0 = x^3 – 4x^2 + 3x – 12
x = 4 , 1.732i, -1.732i

Solving for x, we will have three value one real and 2 imaginary values. Since time cannot be negative and imaginary. The answer would be 4. After 4 years, the company will break even.

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