# Homework Help: Polynomial inequality

1. Sep 29, 2011

### Wa1337

1. The problem statement, all variables and given/known data
4x5-16x4+9x3+23x2-15x-9 > 0

2. Relevant equations
Synthetic division
PQ Rule?

3. The attempt at a solution
Don't know how or where to begin

2. Sep 29, 2011

### gb7nash

The goal here is to find the zeros. Once you find all zeros, you can plug in an arbitrary value between each zero. Do you know the rational root theorem?

3. Sep 29, 2011

### Wa1337

The Pq rule ?

4. Sep 29, 2011

### SammyS

Staff Emeritus
[STRIKE]There are no rational roots. There are 3 real roots & 2 complex roots which aren't real.

Are you sure this is the correct polynomial?[/STRIKE]

Never mind. (I cut & pasted it incorrectly! DUH)

All 5 roots are real. 3 of them are rational.

Last edited: Sep 29, 2011
5. Sep 29, 2011

### Wa1337

Yes this is the correct polynomial given to us for our test review.

REVISED: Okay, well I used synthetic division with the whole polynomial and used the -1 as a factor and it worked well, but now I have 4x4-20x3+29x2-6x-9. What should I do to get further and am I going in the right direction? Thanks.

Last edited: Sep 29, 2011
6. Sep 29, 2011

### SammyS

Staff Emeritus
Use the rational root theorem (the PQ rule). Then use synthetic division.

7. Sep 29, 2011

### Wa1337

Yeah I got 4x4-20x3+29x2-6x-9

8. Sep 29, 2011

### SammyS

Staff Emeritus
So 4x5-16x4+9x3+23x2-15x-9 = (4x4-20x3+29x2-6x-9)(What) ?

What root did you find? There are two other rational roots & 2 irrational roots. Keep working at it.

Try graphing y = 4x4-20x3+29x2-6x-9 .

9. Sep 29, 2011

### Wa1337

(4x4-20x3+29x2-6x-9)(x-1) is the rest of the equation and ok I'll update you when I continue.

We may not use a calculator.