This site seems to have an easy to understand discussion with some good examples.
Descartes' Rule of Signs
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!
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
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.