Question

Find all roots of y=x^3-64

Answer 1

x = -4i and x = 4i, also x = 4

Explanation:

Rewrite y = x^3-64 as y = x^3 - 64. This can again be rewritten, this time as:

y = (x - 4)(x^2 + 16).

Setting this = to 0, we get x - 4 = 0, whose corresponding root is x = 4, and

x^2 + 16), which has two unequal, imaginary roots: x = -4i and x = 4i.