List the possible rational roots of each equation. Then determine the rational roots.

6x^4+35x^3-x^2-7x-1

The answer in the back of the book is:

-1/3 and 1/2

I know that I'm supposed to use Descartes rule of signs. I found that there was 1 positive zero and 3 or 1 negative zeroes.

I'm a bit confused on how you know exactly how many of each zeroes you are supposed to have. I'm assuming you know by looking at the degree and determining which adds up.

Also, how come the book only states 2 answers?

I used an online calculator that says there are 2 other answers which are:

-3 - 2(2)^(1/2)
and
2(2)^(1/2) - 3

Much help appreciated