Question

Help with polynomials

Answer 1

I know a 5th degree polynomial is like ax^5 + ax^4 + ax^3 + ax^2 + ax + c

Answer 2

Right, and where does a polynomial have a root? When it crosses the 'x-axis' right?

Answer 3

Well "real root" anyways

Answer 4

it is
negative
then positive
then negative
then positive

Answer 5

has a root in between each change in sign
any polynomial is continuous, can't skip numbers

Answer 6

^Indeed

In order to have a real root, we just see how many times the values alternate from - to +

Answer 7

Or + to - of course

Answer 8

So in the table it only flips two time s

Answer 9

Are you sure? Just 2?

Answer 10

well with the numbers given to us at least for p(x)

Answer 11

Well we start at -30 and go to 22....so thats 1 root

and we go from 34 to -130 ....make that 2 roots

And finally we go from that -130 to 222...so I count 3 roots

Answer 12

wows I didnt think of that i was just seeing 2 switches. but didnt think of the change after

Answer 13

So just to make sure I understand this,

Say we have x=1,2,3,4,5,6
p(x)= -55, 100, 200, -225, 300, -325
So this would have;

-55 to 100, 1 root
200 to -225, 2 roots
-225 to 300, 3 roots
300 to -325, 4 roots ?

Answer 14

I would say that is correct!

Answer 15

Alright, sorry just reviewing some things for my Clep test. I take it on Friday D:

Answer 16

Been reviewing like Algebra 2 concepts for the past like month and a half trying to get everything settled out

Answer 17

No problem! And I understand...had to take a clep for english...felt like I was back in 5th grade lol

Answer 18

lool Welp Im taking the College algebra one S: Kinda scared cause like some of these things I am not getting