Question

I know the answer, just need to learn how to solve it
Consider the following.
g(x)=x^3-64/x^224

Find the zeros (if any) of the rational function. (Enter NONE in any unused answer blanks.) Use a graphing utility to verify your answer.

Answer 1

answer are 4 and none.

Answer 2

when the top = 0 we got a 0 function

Answer 3

so long as the bottom doesnt get a bad result

Answer 4

so you replace x by 0?

Answer 5

x^3 -64 = 0

Answer 6

factor the diff of cubes

Answer 7

(x-4)^3

Answer 8

(x-4)(x^2+4x+16) = 0

Answer 9

is what i wrote correct/?

Answer 10

no; you need to factor the 'difference of cubes' not make up a cubic expression from the equation :)

Answer 11

lol

Answer 12

ok, so le't get going from your expression

Answer 13

the right part is irreducible so it doesnt factor or have zeros

the left part is: x-4 = 0, x=4

Answer 14

wait, how you get x-4=0 and x=4?

Answer 15

\[(x^3-64)\]
factor the difference of cubes:
\[(x-4)(x^2+4x+16)\]
solve for zeros since 0(B) = 0 or A(0) = 0

Answer 16

oh i totally forogt about the

Answer 17

\[x-4=0 \implies x=4\]

Answer 18

\[x^2+4x+16 =0 \implies never\]

Answer 19

how you get zero?

Answer 20

Do you mean; How do I determine when each factor equals zero?

Answer 21

yeha

Answer 22

i set each factor equal to zero and solve for x

Answer 23

x-4 =0 when ????

x-4 = 0 ; +4 each side

x-4+4 = 0+4

x-0 = 4

x=4

Answer 24

i understand how you get 4, but i dont get how you get 0

Answer 25

soosfgosgoasogosrgoi.......

Answer 26

ok....

tell me, does:

\[0*anything=0?\]

Answer 27

got it

Answer 28

i got another problem simillar to this one

Answer 29

:) what is it

Answer 30

g(x)=x^3-1/x^2+6

Answer 31

same question

Answer 32

x^3-1
------ = 0 when the top =0 right?
x^2+6

Answer 33

yeah

Answer 34

factor the difference of cubes on the top to get:

(x-1) (x^2+x+1)

Answer 35

you get 1, and 0

Answer 36

we know that: 0 * (x^2 +x+1) = 0

and that: (x-1) *0 = 0

Answer 37

thx man, for the help

Answer 38

x-1 = 0; when x=1

x^2+x+1; has no zero value

Answer 39

youre welcome :)

Answer 40

\[x = 2^{(6/227)} \]

Answer 41

A plot supporting the conclusion that x=2^(6/227) is attached.