Question

How do you solve `x(x^2 + 16) = 0`?

Answer 1

`x` = 0

Explanation:

In multiplication, the only way to have `0` as a product is to multiply a number(s) by at least one `0`. Using this property of multiplication, we know that at least one of the terms is equal to `0`:

`x` = 0 | `x^2` + 16 = 0

To solve for the second term, first subtract `16` from both sides of the equation, giving us:

`x^2` = -16

However, there is no real number that can be squared to equal a number lower than `0`, so there is no real solution for the second term.

Answer 2

Shown below

Explanation:

We know if `ab=0`

Then `a= 0` or `b = 0`

`color(red)(=> x = 0`

`=> x^2 + 16 = 0`

`=> x^2 = -16`

`color(blue)(=> x = pm 4i`

If `x in RR -> x = { 0 }`

if `x in CC -> x = { 0 , 4i , -4i }`