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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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
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.
inf ... infinity
ahhh... I'm an idiot . Makes much more sense now. Thanks a lot for the help!
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