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Math Help - Intermediate Value theorem application

  1. #1
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    Intermediate Value theorem application

    Let p(x) be an odd-degree polynomial function. Prove that p(x)=0 has at least one real solution
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  2. #2
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    Not sure if there is a formal proof of this, but one can see that as x \to \infty then p(x) \to \infty and as x \to -\infty then p(x) \to -\infty. (assuming leading coefficient is positive, if negative its just the other way around)

    By definition any polynomial is continuous on \mathbb{R} and thus by the IVT we can say there exists at least one x \in \mathbb{R} such that p(x)=0
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