Question 1134149
Original function has 4 sign changes so 4,2,0 positive roots
f(-x)=x^4-3x^3+2x^2-x+1 or no sign changes so 0 negative roots
rational roots can be factors of 1 divided by factors of 4
so they can be +/- 1, 1/2 and 1/4.  But no negative roots, so they can be +1/4,1/2,1
look at 1 first since easiest to check
1
 /4   -3     +2   -1   1
--4----1-----3----2----3 doesn't work (4-3+2-1+1 doesn't equal 0)
1/4
  4   -2     3/2  -1/4 15/16
1/2
  4    -1    -1/2  -5/4  doesn't work
There are 0 rational roots, 0 positive roots and the 4 roots are all complex (2 conjugate pairs.)  The graph should not touch the x-axis. 

{{{graph(300,300,-10,10,-10,10,4x^4-3x^3+2x^2-x+1)}}}