Question

How do you find all the zeros of `3x^3-4x^2+8x+8` given the zero: `1-sqrt 3i`?

Answer 1

`x = -2/3 and (1+-i sqrt 3)`.

Explanation:

Complex roots occur in conjugate pairs.
So, two of the roots are `1+-i sqrt 3`.
The sum of these roots = 2..

The sum of the three roots is
`-`(coefficient of `x^2`)/(coefficient of `x^3)`=`4/3`.

So, the third root = `4/3-2=-2/3`..