anonymous
  • anonymous
Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. k = 4; f(x) = 2x^3 - 2x^2 - 3x - 5; Lower bound?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Yes or no are the answer choices
anonymous
  • anonymous
@Loser66
Loser66
  • Loser66
So, you have to solve for the zeros of the function. What are they?

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anonymous
  • anonymous
I'm honestly not sure how to find them
Loser66
  • Loser66
use demos graph to see where they cut x-axis
anonymous
  • anonymous
(2.2,0)
anonymous
  • anonymous
So would the answer be no since it's (2.2,0) and 4 would be a higher bound and not lower bound?
Loser66
  • Loser66
we don't have 0. please check
anonymous
  • anonymous
what do you mean? it cut the x-axis at 2.2
Loser66
  • Loser66
but you can use it. now find f(0) =?
Loser66
  • Loser66
replace 0 into f(x) , what do you get?
Loser66
  • Loser66
|dw:1442536923437:dw|
anonymous
  • anonymous
-5
Loser66
  • Loser66
ok, so f(0) =-5 < 0 , right? now f (2) =?
anonymous
  • anonymous
-3
anonymous
  • anonymous
So what does that mean
Loser66
  • Loser66
that mean from 0 to 2 you still not pass the x-axis, since f(x) <0 for both. Now test f(3)
anonymous
  • anonymous
22
Loser66
  • Loser66
yes, so from 2 to 3 , f(x) go from negative to positive, that is you have one zero on that interval, right?
Loser66
  • Loser66
Now, use synthetic,
Loser66
  • Loser66
forget it, short cut
anonymous
  • anonymous
okay haha
Loser66
  • Loser66
|dw:1442537533408:dw|
Loser66
  • Loser66
now, fill up
anonymous
  • anonymous
Again, the lesson didnt really explain this stuff so I'm not sure how to use that
Loser66
  • Loser66
you don't know synthetic?
anonymous
  • anonymous
not completely, looking it up now trying to learn real quick
Loser66
  • Loser66
|dw:1442537680182:dw|
Loser66
  • Loser66
|dw:1442537714109:dw|
Loser66
  • Loser66
now 4 *6 =?
anonymous
  • anonymous
24
Loser66
  • Loser66
|dw:1442537779766:dw| got it?
Loser66
  • Loser66
the last one, you do, the same
anonymous
  • anonymous
would it be 4*21 = 84 or 4*24 =96?
Loser66
  • Loser66
|dw:1442537857152:dw|
Loser66
  • Loser66
you take 4 * the bottom row, put the result on the middle row of the new column, then add them up to get the new number.
anonymous
  • anonymous
oh okay i see
anonymous
  • anonymous
that's easy then haha
Loser66
  • Loser66
|dw:1442538058710:dw|
Loser66
  • Loser66
ok, now, 4 >0 , right?
anonymous
  • anonymous
yes
Loser66
  • Loser66
look at the bottom row, they are 2,6,21,79 right?
anonymous
  • anonymous
yes
Loser66
  • Loser66
and all them are positive, right?
anonymous
  • anonymous
yes
Loser66
  • Loser66
Hence 4 is upper bound for the zeros
anonymous
  • anonymous
woah i see, a lot goes into it
anonymous
  • anonymous
so back to the original question the answer would be no
Loser66
  • Loser66
yup
anonymous
  • anonymous
ok thanks for all of the help, what would happen if one of them was negative?
Loser66
  • Loser66
you test, if k <0, the bottom line is +, -,+,- alternatively, then k is lower bound
Loser66
  • Loser66
learn from it http://www.howe-two.com/mathematicat/bound.html

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