Question 982722
<font face="Times New Roman" size="+2">


Positive case:  Two sign changes, so either two positive real roots or zero positive real roots.


Negative case:  *[tex \LARGE (-x)^4\ +\ (-x)^3\ -\ 3(-x)^2\ +\ (-x)\ +\ 2\ =\ 0]


which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^4\ -\ x^3\ -\ 3x^2\ -\ x\ +\ 2\ =\ 0]


Again, two sign changes so there are either two negative real roots or zero negative real roots.


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

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