Question

How do you find the complex roots of `t^3+2t^2-4t-8=0`?

Answer 1

The roots are:

`-2, -2, 2`

Explanation:

`0 = t^3+2t^2-4t-8`

`color(white)(0) = (t^3+2t^2)-(4t+8)`

`color(white)(0) = t^2(t+2)-4(t+2)`

`color(white)(0) = (t^2-4)(t+2)`

`color(white)(0) = (t^2-2^2)(t+2)`

`color(white)(0) = (t-2)(t+2)(t+2)`

So the roots are:

`-2, -2, 2`

There are no non-Real Complex roots.