Question

What are the possible numbers of positive real, negative real, and complex zeros of f(x) = 8x4 + 13x3 − 11x2 + x + 9?

Positive Real: 1 
Negative Real: 3 or 1 
Complex: 2 or 0

 

Positive Real: 2 or 0 
Negative Real: 0 
Complex: 2 or 4  

Positive Real: 3 or 1 
Negative Real: 1 
Complex: 2 or 0  

Positive Real: 2 or 0 
Negative Real: 2 or 0 
Complex: 4, 2 or 0

Answer 1

As is, 2 sign changes in ++-++, so 0 or 2 positive real roots.
With odd degree signs reversed, 2 sign changes in +---+, so 0 or 2 negative real roots.

The last selection is the correct choice based on the rule of signs.
Positive Real: 2 or 0
Negative Real: 2 or 0
Complex: 4, 2, or 0

_____
A graph shows there are actually 2 negative real roots and 2 complex roots.