SOLUTION: factor the polynomial completely P(x)=x^3-8 what are all the real zeros? what are the positive complex zeros what are the negative complex zeros

Question 977701: factor the polynomial completely
P(x)=x^3-8
what are all the real zeros?
what are the positive complex zeros
what are the negative complex zeros
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
P(x)=x^3-8
what are all the real zeros?
what are the positive complex zeros
what are the negative complex zeros
---------------
P(x) = (x-2)*(x^2 + 2x + 4)
x = 2
============
x^2 + 2x + 4 = 0

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 -12 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 -12 is + or - .

The solution is , or
Here's your graph:

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