# Finding the zeroes for cubic equation

## Homework Statement

Find all zeroes for the function f(x)

f(x)=x^3+25x

## The Attempt at a Solution

I tried factoring out x out of it.

x(x^2+25)

and again to give

x[(x+5i)(x-5i)]

this would give me the 0,-5i,+5i as the zeroes. Doesn't seem to be right though.

Any thoughts?

Thanks!

Last edited:

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

Find all zeroes for the function f(x)

f(x)=x^3+25x

## The Attempt at a Solution

I tried factoring out x out of it.

x(x^2+25)

and again to give

x[(x+5i)(x-5i)]

this would give me the 0,-5i,+5i has the zeroes. Doesn't seem to be right though.

Any thoughts?

Thanks!

Try substituting in your three solutions, to see if they work. You should always check your solutions this way, and you can certainly do it as easily as we can.

(5i)^3+25(5i)=
-125i+125i=0

(-5i)^3+25(-5i)=
125i-125i=0

0^3+25(0)=0

seems to check out for me. however this is not giving me the correct answer according to the solution

Ray Vickson
Homework Helper
Dearly Missed
(5i)^3+25(5i)=
-125i+125i=0

(-5i)^3+25(-5i)=
125i-125i=0

0^3+25(0)=0

seems to check out for me. however this is not giving me the correct answer according to the solution

Your solution is correct, so that must mean that the solution you were given is wrong.

Thanks for your help. Sure is frustrating when you start doubting yourself. Take care.

Mentallic
Homework Helper
You could also have checked the incorrect solutions you were given for peace of mind.