Possible roots? help

Question

P(x) = 3x5 + 3x4 + 2x2 - 4
Possible Roots:  

 

Use Descartes' Rule of Signs to analyze the zeros of the following. List all possibilities.

Answer 1

3x⁵ + 3x⁴ + 2x² - 4

 

Signs: + + + - , one sign change so one positive real root.

 

Let y = -x

 

-3y⁵ + 3y⁴ + 2y² - 4

 

Signs: - + + - , two sign changes so 0 or 2 negative real roots.

 

Thus there are two possibilities here:

 

A: 1 positive real root and 4 complex roots.

 

B: 1 positive real root, 2 negative real roots, and 2 complex roots.