Question

Find the upper and lower limits of the zero of the following function. x^5-3x^3+24 plz explain, especially how to do the synthetic divison??

Answer 1

5 4 3 2 1 0
1 0 -3 0 0 24

with synthetic we should line up our exponents with their coefficients

Answer 2

this gives us a platform to work off of

Answer 3

1 0 -3 0 0 24
0 add this row
-----------------
zero | multiply this row

Answer 4

if we choose a proper amount for our "zero" there will be no remainder on the end

Answer 5

any questions so far?

Answer 6

since the first coeff is a 1; lets get the factors of the last term: 24

1,24
2,12
3,8
4,6

and try them out ... as out zeros

Answer 7

1 0 -3 0 0 24
0 2 4 2 4 8
-----------------
2 | 1 2 1 2 4 32, not a zero and since they are all positive
values we know that the solution aint
greater than a 2 at least

Answer 8

lets try a 1

1 0 -3 0 0 24
0 1 1 -2 -2 -2
-----------------
1 | 1 1 -2 -2 -2 22 ; aint a 1

Answer 9

lets try a -2

1 0 -3 0 0 24
0 -2 4 -2 4 -8
-----------------
-2| 1 -2 1 -2 4 16 , not a -2

it might not even be an integer value

Answer 10

so what does that mean? that it's an x or something?

Answer 11

http://www.wolframalpha.com/input/?i=x^5-3x^3%2B24

Answer 12

it means that it gets ugly

Answer 13

the graph shows that its got a root someplace between -2 and -2.5

Answer 14

lol...why can math never be easy

Answer 15

:) the world is to complicated for math to model it with ease

Answer 16

lol I just wish sometimes my math didn't ask me to be psychic xD

Answer 17

im not quite sure what it means by upper and lower limit tho

Answer 18

I think it means the bounds

Answer 19

the zero is greater than some number and less than some other number at the same time

Answer 20

i have to find those two numbers somehow

Answer 21

lets try a -3

1 0 -3 0 0 24
0 -3 9 -18 54 -162
-------------------
-3| 1 -3 6 -18 54 -138; well, its a + result at "-2" and a
a - result at "-3"

so if anything id say its in the interval: (-3,-2)

Answer 22

a rather simple way to do this is just to try and err it till you get in the right ball park of the area

Answer 23

f(x) = x^5 -3x^3 +24

f(-2) = = (-2)^5 -3(-2)^3 +24 = 16

f(-2.5) = (-2.5)^5 -3(-2.5)^3 +24 = -26.78125

its between -2 and -2.5

try -2.3

f(-2.3) = (-2.3)^5 -3(-2.3)^3 +24 = -3.862...

still on the left of zero; go right a little

f(-2.2) = (-2.2)^5 -3(-2.2)^3 +24 = 4.407

and "zero" in on it till youre close enough

Answer 24

usually you have a "error" allowance so that you can provide a range; with a low and high boundary.

without knowing the error allowance, its hard to say what a good interval will be

Answer 25

I love how my math book does this to me. T.T

Answer 26

thanks for the help

Answer 27

yep, good luck :)