SOLUTION: The question wants you to find the complex zeros and factor the polynomial in standard form: F(X) = x^3 - 1.

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Question 381141: The question wants you to find the complex zeros and factor the polynomial in standard form: F(X) = x^3 - 1.
Answer by neatmath(302)   (Show Source): You can put this solution on YOUR website!

We can easily see that is the difference of two cubes!





set f(x) equal to zero, so we have

or



or



This will involve imaginary numbers because there are NO real numbers which satisfy this equation, but we can use the quadratic formula to find the complex solutions involving imaginary numbers:

Solved by pluggable solver: SOLVE quadratic equation with variable
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

Here's your graph:
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