A company's Profit (in millions of dollars) can be represented by x^2-5x+6, where x is the number of years since the company has started. When did the company have a profit of $2 million?

Given that the profit is represented by:

P (x) = x^2-5x+6

where x is time in years, the time when the profit was $2 million will be evaluated as follows:

from:

P (x) = x^2-5x+6

substitute P (x) = 2

thus

2=x^2-5x+6

simplifying this we get:

x^2-5x+6-2=0

x^2-5x+4=0

factoring the above we obtain:

x^2-x-4x+4=0

x (x-1) - 4 (x-1) = 0

(x-1) (x-4) = 0

hence

x=1 or x=4

Thus the company made $2 million at time x=1 year and x=4 years