Finding the zeroes for cubic equation

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SUMMARY

The cubic function f(x) = x^3 + 25x has three zeroes: 0, -5i, and +5i. The solution was derived by factoring the equation into x(x^2 + 25), which further factors into x[(x + 5i)(x - 5i)]. Verification of these zeroes confirms their accuracy, as substituting them back into the original function yields zero. The initial confusion arose from a discrepancy with an incorrect provided solution.

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Homework Statement



Find all zeroes for the function f(x)

f(x)=x^3+25x

Homework Equations


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!
 
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dmoney123 said:

Homework Statement



Find all zeroes for the function f(x)

f(x)=x^3+25x


Homework Equations





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
 
dmoney123 said:
(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.
 
You could also have checked the incorrect solutions you were given for peace of mind.
 

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