Question

What are the real and complex solutions of the polynomial equation x^3 - 64 = 0

Answer 1

Note that, x = 4 is a solution for the equation.

Then, you can use this value to factored the equation as follows

$x^3 - 64 = (x-4)(x^2 +4x +16) = 0$

Now you need solve

$x^2 +4x +16 = 0$

$x = \frac{-b \pm \sqrt{b^2 -4ac} } {2a} = \frac{-4 \pm \sqrt{16 -64} } {2} = \frac{-4 \pm \sqrt{-48} } {2} = \frac{-4 \pm 4i\sqrt{3} } {2} =-2 \pm2i\sqrt{3}$

Therefore, the solutions are

$4, -2+2i\sqrt{3}, -2-2i\sqrt{3}$.

Answer 2

Answer:

The answer is C on connexus :)

Explanation:

Your welcome, saves time:)