Question

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

Answer 1

Answer:

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

Step-by-step 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:

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