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Math Help - Math question involving polynomials

  1. #1
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    Math question involving polynomials

    The profit, "P", of a video company (in thousands of dollars), is given by P(x) = -5x^2 + 550x - 5000, where x is the amount spent on advertising, in thousands of dollars.

    a) Determine the amount spent on advertising that will result in a profit of $0.

    Ok so I started it here...

    0 = -5x^2 + 550x - 5000
    = -5(x^2 - 110x + 1000)

    I'm not sure how to continue from here. I'm pretty sure that I'm on the right track. I think that you have to find when x = 0. Essentially what I'm trying to do I think is find the x-intercepts.
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  2. #2
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    You have a quadratic equation.
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  3. #3
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    You're on the right track. First of all you can cancel out -5 to give x^2-110x+1000=0 and solve the resulting quadratic using your favourite method .
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  4. #4
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    What do you mean by "favourite method"? Oh wait a minute I think I know what to do. I'll use the formula that I just saw on the wiki link you gave me "emakarov". thanks.

    But firstly how do I cancel out -5?
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  5. #5
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    If you have an equation -5 * f(x) = 0 for some expression f(x), divide both sides by -5 to get f(x) = 0.
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  6. #6
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    So it's just 0 = x^2 - 110x + 1000 ?
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  7. #7
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    Quote Originally Posted by Arise01 View Post
    So it's just 0 = x^2 - 110x + 1000 ?
    Yes.
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  8. #8
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    but what happened to the -5?
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  9. #9
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    Quote Originally Posted by Arise01 View Post
    but what happened to the -5?
    If we have -5(x-a)=0 then (x-a)=0.

    \frac{0}{-5}=0~.
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  10. #10
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    So I use the quadratic formula on x^2 - 110x + 1000 to solve for the x- intercepts?
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  11. #11
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    Quote Originally Posted by Arise01 View Post
    So I use the quadratic formula on x^2 - 110x + 1000 to solve for the x- intercepts?
    Why not just factor it?
    x^2-110x+1000=(x-10)(x-100)
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  12. #12
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    Oh wow how could I miss that. So the x - intercepts are 10 and 100?
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  13. #13
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    Quote Originally Posted by Arise01 View Post
    Oh wow how could I miss that. So the x - intercepts are 10 and 100?
    Right on!
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