What are the real and complex solutions of the polynomial equation?

Question

x3 – 64 =0

(1 point)
Responses

4 comma minus 1 plus 2 lower i Start Root 3 comma End Root minus 1 plus 2 lower i Start Root 3 End Root
Image with alt text: 4 comma minus 1 plus 2 lower i Start Root 3 comma End Root minus 1 plus 2 lower i Start Root 3 End Root

4 comma 1 plus 2 lower i Start Root 3 comma End Root 1 plus 2 lower i Start Root 3 End Root
Image with alt text: 4 comma 1 plus 2 lower i Start Root 3 comma End Root 1 plus 2 lower i Start Root 3 End Root

4 comma minus 2 plus 2 lower i Start Root 3 comma End Root minus 2 minus 2 lower i Start Root 3 End Root
Image with alt text: 4 comma minus 2 plus 2 lower i Start Root 3 comma End Root minus 2 minus 2 lower i Start Root 3 End Root

4 comma minus 2 plus 2 lower i Start Root 3 comma End Root 2 plus 2 lower i Start Root 3 End Root

Answer 1

The real solution of the polynomial equation x^3 - 64 = 0 is x = 4.

The complex solutions are x = -1 + 2i√3 and x = -1 - 2i√3.

So, the complete solutions are x = 4, x = -1 + 2i√3, and x = -1 - 2i√3.