anonymous
  • anonymous
Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = -2x4 + 4x3 + 3x2 + 18
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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welshfella
  • welshfella
+18 * -2 = -36 so you need to list the factors of -36
welshfella
  • welshfella
eg +/- 1 , +/- 2 , etc
anonymous
  • anonymous
±6,±6 ±2,±18 ±3,±12 ±4,±9

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anonymous
  • anonymous
Right?
anonymous
  • anonymous
@welshfella
Nnesha
  • Nnesha
hmm
anonymous
  • anonymous
?
Nnesha
  • Nnesha
hmm ho would that work ? are we going to divide all factors by 2 maybe
Nnesha
  • Nnesha
how**
Nnesha
  • Nnesha
p/q method \[\rm \frac{ p }{ q }=\frac{ \pm~ list~factors~of~ constant~term }{\pm~ list ~factors~of~leading ~coefficient }\]
welshfella
  • welshfella
ah yes - i'd forgotten that formula. So +/- 18 would not be included
anonymous
  • anonymous
So I divide all those numbers by 2?
welshfella
  • welshfella
- to be honest I'm not sure ....
Nnesha
  • Nnesha
no i was asking should we divide by 2..
welshfella
  • welshfella
It's been a long time since i did these
Nnesha
  • Nnesha
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
welshfella
  • welshfella
i suppose 18 would be included as its 18 / 1
welshfella
  • welshfella
???
Nnesha
  • Nnesha
what do you mean welshfell ? sorry i don't get it .. :o
welshfella
  • welshfella
well 18 is a factor of the constant term and 1 is a factor of -2
anonymous
  • anonymous
Yes, you would include 18 for precisely the reason you just described.
welshfella
  • welshfella
I guess I should revise this stuff!!!
Nnesha
  • Nnesha
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
welshfella
  • welshfella
yea
Nnesha
  • Nnesha
\[\rm \frac{p}{q}= \frac{ \pm 1 , \pm 2 , \pm 3,\pm 6, \pm 9,\pm 18}{\pm 1 , \pm2}\] now just divide and remember each number at the numerator are dividing by1 and 2
Nnesha
  • Nnesha
ofc +/- 1 , +/- 2
welshfella
  • welshfella
yes thats it
anonymous
  • anonymous
±1, 2, 3, 6, 9, 18, 1/2, 3/2, 9/2
welshfella
  • welshfella
Of course its possible that none of those are roots but that'f not relevant to the question.
Nnesha
  • Nnesha
^^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
welshfella
  • welshfella
Just out of interest I'll do this one on my calc...
anonymous
  • anonymous
So what I posted should be the answer that's needed for this question?
Nnesha
  • Nnesha
yes
Nnesha
  • Nnesha
ye use calculator for real zeros ;P
anonymous
  • anonymous
Thank you two
welshfella
  • welshfella
real zeros are 2.89 and -1.524 the other 2 roots are complex
welshfella
  • welshfella
yw

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