Question

Use Descartes' rule of signs to describe possible combinations of roots for the polynomial h(x)=2x^3+5x^2-31x-15

Answer 1

http://www.purplemath.com/modules/drofsign.htm

see if this helps and let me know

Answer 2

would there be 2 combinations of roots?

Answer 3

one positive root...

Answer 4

2 or 0 negative roots

Answer 5

h(x)= + 2x^3 + 5x^2 - 31x - 15
no yes no

signs changed only once, so 1 or 0 real positive roots

now checking f( -x )
h( -x)= - 2x^3 - 5x^2 + 31x - 15
no yes yes

it changed signs twice, so 2 or 0 negative real roots

Answer 6

what do you mean by 2 or 0 negative roots?

Answer 7

hmm one sec... shoot... I missed the \(x^2\)

Answer 8

not 1 or 0 positive root, 1 positive root

Answer 9

now checking f( -x )
h( -x)= - 2x^3 + 5x^2 + 31x - 15
yes no yes

it changed signs twice, so 2 or 0 negative real roots

Answer 10

I'm really confused now! For the function h(x)=2x^3+5x^2-31x-15, it asked for the possible combinations of roots, so the possible combinations are only 1 positive root, and 2 or 0 negative roots?

Answer 11

complex roots always come in conjugate pairs whenever a polynomial has real coefficients so you have to account for that possibility.

if there are 2 negative roots, then they're real.

otherwise, the polynomial may have to complex roots and in that case they would not cross the x axis anywhere (in the real cartesian coordinates)

Answer 12

oh okay @pgpilot326! that makes sense :)

Answer 13

"two", not "to"

Answer 14

always count down the number of changes from the max, by two to account for possible conjugate pairs.

so if you came up with 3 changes, then the possibilities are 3 or 1 (counting down by 2).

Answer 15

okay :) so again, just to confirm the answer i put down 1 positive root and 2 or 0 negative roots for the possible roots?

Answer 16

you got it girl!

Answer 17

thank you so much! you're awesome! :)

Answer 18

\[\tiny\text{Lana...}\]
\[\small\text{Lana...}\]
\[\text{Lana...}\]
\[\large\text{Lana...}\]
\[\huge\text{Lana!!!}\]

"What!!!"

\[\small\text{Danger Zone!}\]

Answer 19

You are!

Answer 20

Haha! Thank you :)

Answer 21

I take it you've seen Archer?

Answer 22

I can't remember when, but yeah! :)

Answer 23

cool. keep at it!

Answer 24

thanks i will, you too! :)