Find the complex zeros of the following: x^3 + 216

Write in factored form.

Question

Find the complex zeros of the following: x^3 + 216

Write in factored form.

anonymous · Answer

Does this equation equal anything?

anonymous · Answer

no

anonymous · Answer

Refresh my memory.  A "complex zero" is of the form a +bi, which makes the given equation =0, correct?

anonymous · Answer

yes

anonymous · Answer

216 is 6 cubed. So the zeros are going to be six times the zeros of x^3 + 1=0. Can you do that problem?

anonymous · Answer

Since you want the zeros, we should set the equation equal to 0 and solve by factoring.
we get:
$$x^{3}+216 = (x+6)(x^{2}-6x+36)=0$$
Now we set both of those terms equal to 0, but the left term isnt going to produce a complex root:
$$x^{2}-6x+36 = 0 \Rightarrow x = \frac{6\pm \sqrt{36-4(36)}}{2} = 3 \pm 3i \sqrt{3}$$
If you want me to show more work let me know :)

myininaya · Answer

(x+6)(x^2-6x+36)=0