Profit and break-even ?

Question

How to find break-even points of profit function?

Which of the following profit functions has break-even points at x = 3 and x = 11?

a) P(x) = -2 (x^2 - 28x + 66)

b) P(x) = -2 (x + 3)(x + 11)

c) P(x) = -2 (x - 3)(x + 11)

d) P(x) = -2(x^2 - 14x + 33)

I have tried to solve this by completing the square for a and d because I don't think b and c are possible answers and it did not work out I tried and tried again. If someone knows the answer could you please show/explain the steps in addition to naming the appropriate letter answer. Thanks in advance.

Answer 1

I don't think you need to complete the squares. I agree that b and c are not possible answers. I just put the values of x=3 and x=11 in equations a and d to test.

Equation d was the only one in which P(3) = P(11) = 0.

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Factoring Equation d) gives:

-2(x^2 - 14x + 33) = -2 * (x - 11) * (x - 3)