Finding the Zeros of a Polynomial Function

[jai6638]

hey.. how would i find the zeros of the following function:

f(x)=x^4-25

I tried inputting the value into my caculator and then go to table find y values that equal 0 in x and i only found -25.. how do i find the rest?


thanks

 

[jamesrc]

-25 shouldn't be one of the zeros. You can find the two real zeros graphically, but why not do it algebraically?

x⁴ - 25 = 0
x⁴ = 25
x² = {-5, +5}
and so on...

 

[vitaly]

$$x^4-25=0$$
$$x^4=25$$
$$x^2=5$$
$$x=+-/sqrt{5}$$

 

[klusener]

hey vitaly, do you by any chance live in Ohio? just guessing...

 

[vitaly]

Nope... What makes you say that?

 

[klusener]

i knew a person by the name Vitaly there, but i guess it is a common name.. so i was being unrealistic...

 

[vitaly]

Oh, well I live in TN...

Is the person you knew Russian? I have never met anybody else with my name before. Most people think it's weird; it's definitely not common here.

 

[klusener]

yup, they were russians.. infact there was two of them cause they were twins...

 

[jai6638]

ok that was a stupid question... didnt think of that for some odd reason.. thanks much for ur help1

 

[Hurkyl]

For the sake of precision, from:

x^4 = 25

you should deduce

x^2 = 5 or x^2 = -5

and not just the first one.


Actually, I'm a big fan of using factoring instead of these types of manipulations. e.g.

x^4 = 25
x^4 - 25 = 0
(x^2 - 5)(x^2 + 5) = 0

 

[dextercioby]

To continue from where Hurkyl left off:

$$x^{4}-25=(x-\sqrt{5})(x+\sqrt{5})(x-i\sqrt{5})(x+i\sqrt{5})=0$$

I think the solutions are obvious.

Daniel.

 

[iodmys]

To continue from where Hurkyl left off:

$$x^{4}-25=(x-\sqrt{5})(x+\sqrt{5})(x-i\sqrt{5})(x+i\sqrt{5})=0$$

I think the solutions are obvious.

Obvious? Probably not to jai6638

 

[dextercioby]

And how did u know that??Did u talk to him??

Daniel.

 

[jai6638]

i got it... thanks much! :)

 

[iodmys]

And how did u know that??Did u talk to him??

Daniel.

Well, he(she?) didn't know how to find the zeros of x^4-25. From that I can infer that you statement might not be very obvious to him(her?).