Question

Least upper bound , Greatest lower bound

Answer 1

@ganeshie8

Answer 2

https://www.youtube.com/watch?v=XgGzm0d_MDY

Answer 3

watch this quick,
we can do an example after that :)

Answer 4

I watched it >.<

Answer 5

The same on u sent last night?

Answer 6

no, this is different and much better and short

Answer 7

7 minutes.... watch it :)

Answer 8

Okay, So i have a feeling that -1 will be one of the answers because that is one of the factors that did not have remainder 0

Answer 9

\[x^4+10x^3+33x^2+38x+8\]

Answer 10

yes, we have found roots for this already right ?

Answer 11

Yes but we did not find bounds

Answer 12

atleast i dont think we did

Answer 13

once we have roots, finding bounds is piece of cake

Answer 14

Well lets bake a cake then! lol

Answer 15

lol, below are ur roots :

\(\large -4, ~-2, ~-2-\sqrt{3}, -2 + \sqrt{3}\)

Answer 16

whats the lowest value ?
whats the greatest value ?

Answer 17

the lowest value of roots is \(-4\),
so the "greatest lower bound" is \(-4\)

Answer 18

the highest value of roots is \(-2 + \sqrt{3}\)
so the "least upper bound" is \(-2 + \sqrt{3}\)

Answer 19

we're done.

Answer 20

let me knw if smthng doesnt make sense..

Answer 21

Do you want ice cream with your cake?

Answer 22

Because im going to reward myself for understand what you just said muhaha

Answer 23

Shall we do another?

Answer 24

Oh, you left ( ._.)

Answer 25

awww both are irresitables xD

Answer 26

sorry somebody knocked the door... had to attend to that lol

Answer 27

lets do the next q :)

Answer 28

"Attend to that " sounds like you murdered them haha

Answer 29

lol hahah wish i could >.<

Answer 30

wats the next q ha ?

Answer 31

Lol nice way to change the subject ;)

Answer 32

sec itll take a second to type

Answer 33

:) take ur time

Answer 34

\[p(x)=x^5+3x^4-9x^3-3x^2-52x-60\]

we need to find :
p
q
p/q
# of positive roots
# of negative rootss
least upper bound
greateest lower bound
roots

Answer 35

evil professor :/

Answer 36

seriously though. that 60 is about to make me cry

Answer 37

start by counting sign changes in p(x) and p(-x)

Answer 38

1?

Answer 39

\(p(x)=x^5+3x^4-9x^3-3x^2-52x-60\)

yes, sign changes in p(x) = 1
so there will be EXACTLY 1 positive real root for p(x)

Answer 40

next, find f(-x), and count the sign changes

Answer 41

its either 2 or 6

Answer 42

Is that not right?

Answer 43

\(p(x)=x^5+3x^4-9x^3-3x^2-52x-60 \)

\(p(-x)=-x^5+3x^4+9x^3-3x^2+52x-60 \)

Answer 44

sign changes in p(-x) is 4
so there can be 4 or 2 or 0 negative real roots

Answer 45

Yeah i knew that, I was just testing you

Answer 46

P = 60
Q = 1

P/Q = \(\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, ......\)

Answer 47

>.>

Answer 48

pick ur fav number

+1 or -1 ?

Answer 49

-1

Answer 50

\(
\begin{array}{}

-1|&1&3&-9&-3&-52&-60\\
&&&&\\
\hline
&&&&\\
&1&&&

\end{array}
\)

Answer 51

ill do it !