Question

Couldn't find a root for P(x)=2x^4-x^3-14x+17...asking for all rational roots for P(x)=0

Answer 1

Did you try synthetic division with all the possible rational roots?

Answer 2

Yes

Answer 3

Did you remember to put in the 0 for 0x^2 ??

Answer 4

Lol! ty

Answer 5

However, it has no rational roots:
http://www.wolframalpha.com/input/?i=Solve%3A2x^4-x^3-14x%2B17%3D0

Answer 6

I also noticed that i wrote 17 instead of 7.

Answer 7

Well, that's a whole different thing.

Answer 8

Now you can factor by grouping.

Answer 9

How do you do that?

Answer 10

I think if you graph the curve you'll find its positive definite

Answer 11

so it won't have any rational roots

Answer 12

\[2x^4-x^3-14x+7=x^3(2x-1)-7(2x-1)=(2x-1)(x^3-7)=0\]

Answer 13

We didn't learn the graphing part for this lesson yet

Answer 14

is it +17 or +7..?

Answer 15

So:
\[2x-1=0; x=\frac{1}{2}\]

Answer 16

@campbell_st If you read the previous posts, your question will be answered

Answer 17

And that is the only rational root.

Answer 18

Did you understand the "factor by grouping" part?

Answer 19

Yes, you took out from the paranthesis so it became x^3(2x.... etc

Answer 20

very good.

Answer 21

:)

Answer 22

Quick question, when using synthetic division, lets say you're using a 2 to multiply into the following numbers, do you turn that 2 into a negative 2?

Answer 23

If 2 is a 0, 2 is the shelf number
If x+2 is a factor, -2 is the shelf number.

Answer 24

ohh ok

Answer 25

When using synthetic division does the 0 always have to be at the end? or can it be in the middle ?

Answer 26

It has to be at the end, because that means that the remainder of the division problem is 0. Or, in other words, you have found a factor because the problem "came out even"

Answer 27

kk ty

Answer 28

yw