Question

How do you find the complex roots of `x^4-10x^2+9=0`?

Answer 1

The roots are `+-3` and `+-1`

Explanation:

Note that `9+1 = 10` and `9*1 = 9`.

Hence we find:

`0 = x^4-10x^2+9`

`color(white)(0) = (x^2-9)(x^2-1)`

`color(white)(0) = (x^2-3^2)(x^2-1^2)`

`color(white)(0) = (x-3)(x+3)(x-1)(x+1)`

So the four roots of this quartic equation are `+-3` and `+-1`

These are Real numbers, but any Real number is also a Complex number (of the form `a+0i` if you wish).