Question 989860
<font face="Times New Roman" size="+2">


Write the equation as a function:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ x^4\ -\ x\ -\ 5]


Check a few values.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(0)\ =\ -5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(1)\ =\ -5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(2)\ =\ 9]


By the intermediate value theorem, since 0 is between -5 and 9, there must be a value *[tex \Large x] between 1 and 2 such that *[tex \Large f(x)\ =\ 0]


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

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \