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

Question

1748 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-22T03:05:53

#{0,2,-2,2i,-2i}#

#3x^5-48x = 0 implies#

#3x(x^4-16) = 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 {2,-2,2i,-2i}#

The entire solution set is

#{0,2,-2,2i,-2i}#

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

#{0,2,-2}#