Question

can someone remind me how to use descartes's rule of signs? i need to learn it for the solutions of higher order linear DE :/

Answer 1

i just need a *brief* review of the rule

Answer 2

I found the following brief definition.
No algegraic equation f(x) = 0 can have more positive or negative roots respectively than there are changes of sign from + to - and from - to + in the polynomial f(x) or f(-x)

Answer 3

could you demonstrate how to use it?

Answer 4

Coordinate Geometry! correct!

Answer 5

coordinate geometry?

Answer 6

Count sign changes = possible number of + roots (or less by factors of 2)
Put x = -x and count sign changes = possible number of negative roots (or less...)
Rest are complex (up to degree of polynomial and in pairs obviously)

Answer 7

http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs

Answer 8

thanks @estudier just one quesiton. ALWAYS sub x with -x?

Answer 9

ur welcome. Yes (why do you have a doubt?)

Answer 10

just making sure. that it's constant.

Answer 11

Or you can multiply the coefficients of terms with odd power by -1, which is the same thing.

Answer 12

the positive root will just be the number of unchanged signs right?

Answer 13

following the logic that changed signs means negative roots...

Answer 14

Count sign changes = possible number of + roots (or less by factors of 2)

ie number of changes = possible number of .....

Answer 15

Same thing again for negative roots (after putting -x)

Answer 16

wait..if you dont multiply by -1 then the change of signs = number of positive roots?

Answer 17

Do example here:
http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs#Example

Answer 18

ooh okay thanks