# What is the solution set of the equation 3x^5 - 48x = 0?

May 22, 2018

$\left\{0 , 2 , - 2 , 2 i , - 2 i\right\}$

#### Explanation:

$3 {x}^{5} - 48 x = 0 \implies$

$3 x \left({x}^{4} - 16\right) = 0$

Thus, either $x = 0$ or ${x}^{4} - 16 = 0$

For the latter choice, we have four solutions :

${x}^{4} = 16 = {2}^{4} \implies x \in \left\{2 , - 2 , 2 i , - 2 i\right\}$

The entire solution set is

$\left\{0 , 2 , - 2 , 2 i , - 2 i\right\}$

If you want a solution in reals only, then the solution set is

$\left\{0 , 2 , - 2\right\}$