Question

x^3+64=0
A.-4, -2+2i(square root)3 and -2-2i(square root)3
B. -4, 2+2i(square root)3 and 2-2i(square root)3
C. -4, 2+i(square root)3 and 2-i(square root)3
D. -4, 2+2(square root)3 and 2-2(square root)3

Answer 1

Why are you reposting the question?

Answer 2

because no one gave me a correct answer

Answer 3

No one is supposed to give you correct answers, but you should be guided to an answer.

I did in fact tell you how to a) disregard the wrong answers and b) find which of your answer choices is correct.

Answer 4

but i don't know how to find the correct answer so it doesn't help to 'disregard the wrong' when you don't know the wrong

Answer 5

When you have a multiple choice question and you can eliminate all of the wrong answers, that does help you!

Answer 6

In any case, I gave you two ways to solve this: either by eliminating all the wrong answers, or recognizing a correct answer.

Answer 7

\[x^3+64 = 0\]\[x^3 = -64\]\[-4^3 = 64\]I'm not giving anything away there, as all of your answer choices have \(-4\) in them, and its fairly obvious that \(-4*-4*-4 = -64\)

The problem is figuring out the other two roots.

When you look at the complex roots of a problem like this, they are always symmetrically placed in the complex plane:



That's our first root that we found. It's really \(x = -4 + 0i\) where \(i = \sqrt{-1}\)

Answer 8

The other two roots will be placed at equal angles around the circle:

Answer 9

It's just a matter of a bit of trigonometry in an over-sized unit circle to find their coordinates.