Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = -2x4 + 4x3 + 3x2 + 18

Answer 1

Well, do it.

What are ALL the factors of 18? That's where you start.

Answer 2

okay im reaaly confused on this. completly lost. can u help me solve it.

Answer 3

I did. Find ALL the factors of 18. ALL of them.

Answer 4

factors can be 9 and 2??

Answer 5

And 1*18
And 3*6

ALL of them!

Answer 6

18 and 1

Answer 7

Do you have them all?

1*18
2*9
3*6

Is that it?

Answer 8

ya the factors are 1,3,6,9, and 18

Answer 9

Where did 2 go?

Okay, that was the constant term. Now, we need to worry about the highest degree term, -2x^4

All the factors of 2 are 1 and 2. That was a little easier.

The Rational Root Theorem states that Rational Roots, if they exist, are quotients of those two collections. In this case: \(\dfrac{Some\;Factor\;of\;18}{Some\;Factor\;of\;2}\).

Can you build that entire collection?

Answer 10

no u lost me there. so what do i divide. did u slove it?

Answer 11

my test is timed i just really really need help solving it please! i attempted this 4 times already and got it wrong

Answer 12

All the factors of 18. These are 1, 2, 3, 6, 9, 18
All the factors of 2. These are 1, 2
All possible combinations with a factor of 18 in the numerator and a factor of 2 in teh denominator. I don't actually believe you cannot understand this.

1/1, 2/1, 3/1, 6/1, 9/1, 18/1, 1/2, 2/2, 3/2, 6/2, 9/2, 18/2

That's HALF the list.

-1/1, -2/1, -3/1, -6/1, -9/1, -18/1, -1/2, -2/2, -3/2, -6/2, -9/2, -18/2

That's the other half.

If there are rational roots, they MUST be among those listed. Never underestimate the power of something that can count!