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

+18 * -2 = -36

so you need to list the factors of -36

Answer 2

eg +/- 1 , +/- 2 , etc

Answer 3

±6,±6
±2,±18
±3,±12
±4,±9

Answer 4

Right?

Answer 5

@welshfella

Answer 6

hmm

Answer 7

?

Answer 8

hmm ho would that work ? are we going to divide all factors by 2 maybe

Answer 9

how**

Answer 10

p/q method \[\rm \frac{ p }{ q }=\frac{ \pm~ list~factors~of~ constant~term }{\pm~ list ~factors~of~leading ~coefficient }\]

Answer 11

ah yes - i'd forgotten that formula. So +/- 18 would not be included

Answer 12

So I divide all those numbers by 2?

Answer 13

- to be honest I'm not sure ....

Answer 14

no i was asking should we divide by 2..

Answer 15

It's been a long time since i did these

Answer 16

p/q method \[\rm \frac{ p }{ q }=\frac{ \pm~ list~factors~of~ constant~term }{\pm~ list ~factors~of~leading ~coefficient }\]
do this divide factors of constant term by factors leading coefficient

Answer 17

i suppose 18 would be included as its 18 / 1

Answer 18

???

Answer 19

what do you mean welshfell ? sorry i don't get it .. :o

Answer 20

well 18 is a factor of the constant term and 1 is a factor of -2

Answer 21

Yes, you would include 18 for precisely the reason you just described.

Answer 22

I guess I should revise this stuff!!!

Answer 23

f(x) = -2x4 + 4x3 + 3x2 + 18

leading coefficient = -2 so factors are \[\pm 1 , \pm2 \]
constant term is 18= so factors 1 ,2 ,3 , 6,9,18
so we should include all of them

Answer 24

yea

Answer 25

\[\rm \frac{p}{q}= \frac{ \pm 1 , \pm 2 , \pm 3,\pm 6, \pm 9,\pm 18}{\pm 1 , \pm2}\]
now just divide
and remember each number at the numerator are dividing by1 and 2

Answer 26

ofc +/- 1 , +/- 2

Answer 27

yes thats it

Answer 28

±1, 2, 3, 6, 9, 18, 1/2, 3/2, 9/2

Answer 29

Of course its possible that none of those are roots but that'f not relevant to the question.

Answer 30

^^ye that to find real you can use synthetic division or just replace all x's with each possible solution if you get zero as final answer then that would be the real zero

Answer 31

Just out of interest I'll do this one on my calc...

Answer 32

So what I posted should be the answer that's needed for this question?

Answer 33

yes

Answer 34

ye use calculator for real zeros ;P

Answer 35

Thank you two

Answer 36

real zeros are 2.89 and -1.524
the other 2 roots are complex

Answer 37

yw