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

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Answer 1 · 2018-05-22T03:05:53

${0, 2, - 2, 2 i, - 2 i}$ ${0,2,-2,2i,-2i}$

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

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

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

For the latter choice, we have four solutions :

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

The entire solution set is

${0, 2, - 2, 2 i, - 2 i}$ ${0,2,-2,2i,-2i}$

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

${0, 2, - 2}$ ${0,2,-2}$

What is the solution set of the equation 3x^5 - 48x = 03x5−48x=03x^5 - 48x = 0?