Use Descartes rule.
To find the number of positive zeros, we evaluate f(x) and see the number of sign changes.
To find the number of negative zeros, we evaluate f(-x) and see the number of sign changes.
f(x) has no sign change
f(-x) = ax4 - bx3 + cx2 - dx + e
f(-x) has 4 sign changes
Here is your possibilities in a chart:
# of positive zero | # of negative zeros | # of complex zeros
0 4 0
0 2 2