Thread: Descartes rule of signs

Hi again

I am so frustrated - I haven't posted in a while and today this is my 2nd post.

First time I'm doing Descartes rule of signs and it just doesn't make sense.

I get the part where you take the polynomial and count the sign changes to get the max positive number of 0's

The problem comes it with the P(-x) where you then change the polynomial - i do this as I've done everything else where 2 -'s make a + but for some reason this seems to be wrong?

I have a question I have to do but I'd like someone to explain another random example to me - then I'd like to try mine and have you check it for me?

Thanks for all the help guys you rock!

Janine

Originally Posted by Jadekingy

Hi again

I am so frustrated - I haven't posted in a while and today this is my 2nd post.

First time I'm doing Descartes rule of signs and it just doesn't make sense.

I get the part where you take the polynomial and count the sign changes to get the max positive number of 0's

The problem comes it with the P(-x) where you then change the polynomial - i do this as I've done everything else where 2 -'s make a + but for some reason this seems to be wrong?

I have a question I have to do but I'd like someone to explain another random example to me - then I'd like to try mine and have you check it for me?

Thanks for all the help guys you rock!

Janine

Hi Janine,

This site seems to have an easy to understand discussion with some good examples.

Descartes' Rule of Signs

And if the site in the previous link doesn't quite get the job done, Google has plenty of other listings.

Hi there,

thanks for your reply! I visited that site this morning and googled myself silly - I understand most of it but I don't get how the (-x) is done - let me give you an example

put -x in this : 2x^3 + 5x^2 - 4x + 1

this is what my answer would be - but when compared to other examples I'm wrong, I don't understand why:

-2x^3 - 5x^2 + 4x +1

Originally Posted by Jadekingy

Hi there,

thanks for your reply! I visited that site this morning and googled myself silly - I understand most of it but I don't get how the (-x) is done - let me give you an example

put -x in this : 2x^3 + 5x^2 - 4x + 1

this is what my answer would be - but when compared to other examples I'm wrong, I don't understand why:

-2x^3 - 5x^2 + 4x +1

[/quote]
This is where you are making your mistake: (-x)^2= (-x)(-x)= x^2, not -x^2. You should have 2x^3+ 5x^2+ 4x+ 1 which has no sign changes and so no positive roots meaning that the original polynomial has no negative roots.

DesCarte's rule of signs says that 2x^3+ 5x^2- 4x+ 1 has one positive root and no negative roots. That means, of course, that it has two, complex conjugate, complex roots.

In general, an odd power of x changes sign but not an even power.