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a market researcher predicted that the profit function for the first year of a new business would be p(x)= -0.3x^2 + 3x -15, where x is based on the number of items produced. will it be possible for the business to break even in its first year?

thanks

to break even, p(x) = 0
-.3x^2 + 3x - 15 = 0
times -10
3x^2 - 30x + 150=0
x^2 - 10x + 50 = 0
x = (10 ± √-100)/2

this has no real solution, the company will never make a profit.

Where did the "times -10" come from?

in order to break even he would have to produce

5+the square root of 27
5-the square root of 27
because the second answer gives you a negative (you cant produce a negative amount of product) use the first one

10.19615242 is equivalent to x

so unless you can produce and sell .19615242 of a product which i don't know depending on the industry you just might be able, he cant break even.

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