Question

One zero of x^3 - 4x = 0 is 0 what are the other zeros of the function

Answer 1

So you have x^3 - 4x = 0. What you can do is pull out an x from both x^3 and - 4x so it looks like this:

$x( {x}^{2} - 4) = 0$

Then you can find a number that makes the part inside the parentheses turn into zero. For beginners, it may be easier to write it out seperately and solve for x.

${x}^{2} - 4 = 0$

We need to solve for x, so the first step is to add 4 to both sides, so we get something like this:

${x}^{2} = 4$

Then, we can square root both sides to get rid of the power on the x, so it looks like this:

$x = \sqrt{4}$

Now, every square root has two answers, a positive and a negative. If we look at the bottom example:

${2}^{2} = 4$

${( - 2)}^{2} = 4$

We can see that both -2 and 2 to the power of two will equal to 4.

So finally, we get:

$x = - 2 \: and \: 2$

These are the other 'Zero's for the original function. If you are not sure of what a 'Zero' is, it is where the function crosses over the x-axis on a graph.