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Math Help - IVT

  1. #1
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    IVT

    I need to show that the polynomial p(x) =x^3+2x+b, where b is any real number, has a real root by applying the Intermediate Value Theorem. Any ideas? I would greatly appreciate any help.
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  2. #2
    Member Mentia's Avatar
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    the function is continuous. lim (x-> -inf) p(x) = -inf
    lim (x -> +inf) p(x) = +inf

    therefore by the intermediate value thm the function hits all values between -inf and +inf, including zero

    something like that i think
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  3. #3
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    When you say inf, I assume you mean infimum? How does that help? I don't mean to sound unappreciative, I'm just not making the connection.
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  4. #4
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    inf ... infinity
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  5. #5
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    ahhh... I'm an idiot . Makes much more sense now. Thanks a lot for the help!
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