Question 616968
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If


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \text{sgn}\left(f(a)\right)\ \neq\ \text{sgn}\left(f(b)\right)]


where, presuming real function values:


<img class="tex" alt=" \sgn(x) = \begin{cases}
-1 &amp; \text{if } x &lt; 0, \\
0 &amp; \text{if } x = 0, \\
1 &amp; \text{if } x &gt; 0. \end{cases}" src="//upload.wikimedia.org/wikipedia/en/math/2/6/c/26ca3289b0a374f571997861520afd19.png" />


then *[tex \LARGE f(x)] has a real zero on [*[tex \LARGE a,b]]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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