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) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find the complex zeros for f(x) = x^3 - 1
x%5E3+-+1+=+0
%28x-1%29%2A%28x%5E2+%2B+x+%2B+1%29+=+0
x = 1
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x%5E2+%2B+x+%2B+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A1=-3.

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 - sqrt%28+3%29+=+1.73205080756888.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B1+%29

Answer by richard1234(7193) About Me  (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.