Question

Find the roots of the function f(x) = 3x4 - 48.

Answer 1

`x=\pm 2\text{ or } x = \pm 2i`

Explanation:

We are given:

`0=3x^4-48`

Factor:

`0=3(x^4-16)`

Difference of Two Squares:

`0=3(x^2-4)(x^2+4)`

Zero Product Property:

`(x^2-4)=0\text{ or } x^2+4=0`

Solve:

`x^2=4\text{ or } x^2=-4`

Take the square root. Since we are taking an even-root, it requires plus/minus:

`x=\pm 2\text{ or } x = \pm 2i`