all possible roots?

Question

P(x) = 2x5 + 7x3 + 6x2 – 2
Possible Roots:  

 

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

 

Please explain 

Answer 1

maximum 1 positive real zero

maximum 2 negative real zeros

2 or 4 imaginary zeros

1 positive real

0 or 2 negative real zeros

max 3 real, min 1 real,

min 2 imaginary, max 4 imaginary

imaginary zeros always come in conjugate pairs, so they're always an even number

one certainty: there is 1 real positive zero

and it's between 0 and 1, and between 1/3 and 1/2

if there are any negative real zeros they're between 0 and -1,

but an educated guess is there are none