SOLUTION: How do I find the complex zeros for f(x) = x^3 - 1 And then how do I write that in factored form?

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Question 491110: How do I find the complex zeros for f(x) = x^3 - 1
And then how do I write that in factored form?
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
How do I find the complex zeros for f(x) = x^3 - 1


x = 1
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -3 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -3 is + or - .

The solution is , or
Here's your graph:
Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
If you know about roots of unity we can say that







These are just three evenly spaced points on a circle of radius 1 in the complex plane.
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