What does Descartes’ Rule of Signs tell you about the real roots of the polynomial?

–3x^3 + x^2 – x – 6 = 0

There is one positive root and either two or zero negative roots.

There are either two or zero positive roots, and there are either two or zero negative roots.

There is one positive root and one negative root.

There are either two or zero positive roots and one negative root.

Question

What does Descartes’ Rule of Signs tell you about the real roots of the polynomial? 

–3x^3 + x^2 – x – 6 = 0

 
There is one positive root and either two or zero negative roots.

There are either two or zero positive roots, and there are either two or zero negative roots.

There is one positive root and one negative root.

There are either two or zero positive roots and one negative root.

anonymous · Answer

it must be a theorem or a lemma. I remember seeing it in the SAT math book, but I don't precisely remember it. I don't think the proof would be something in our level

anonymous · Answer

How would I be able to solve this with theorem or lemma? Do you have any examples?

anonymous · Answer

http://en.wikipedia.org/wiki/Descartes'_rule_of_signs scroll down and you'll find an example. It's pretty easy to grasp...

anonymous · Answer

So, would it have "two or zero positive roots"? B?

anonymous · Answer

Im a little lost here.

anonymous · Answer

gimme a sec...

anonymous · Answer

k

anonymous · Answer

two positive and one negative

anonymous · Answer

Ah!, so it would be D? How did you solve this?

anonymous · Answer

according to what was said in the wiki. the number of sign changes!

anonymous · Answer

Rechecked the wiki, and it is in fact d, Thank You!

anonymous · Answer

Thanks, I got a medal in my first hour!

anonymous · Answer

Lol, You deserve it!

anonymous · Answer

Thanks! :D