SOLUTION: I am trying to solve this problem but am having some issues. Find all real and imaginary zeros for each polynomial function f(x)=4x^4-1 Here is what I have started but I

Question 88393: I am trying to solve this problem but am having some issues.
Find all real and imaginary zeros for each polynomial function
f(x)=4x^4-1
Here is what I have started but I am unsure if this is right or how to finish it.
f(x)=4x^4-1
4x^4-1=0
+1=+1
4x^4=1
-------
4 4
x^4=-1/4
Thank you for your assistance.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Solve for x:
Do you recognise this as the difference of two squares?

The difference of two squares can be factored thus:
Applying this to your problem, you get:
Now set this equal to zero.
Apply the zero products principle.
or Solve each of these quadratic equations.
Subtract 1 from both sides.
Divide both sides by 2.
Finally, take the square root of both sides.
or
...and for the other equation:
Add 1 to both sides.
Divide both sides by 2.
Take the square root of both sides.
or
So you have two real but irrational roots:

...and two imaginary roots:
which can also be written as:
which can also be written as:
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