List the potential rational zeros of the following function. Please show all work b/c I am not understanding this.
f(x)=7x^4-x^2+3

Question

List the potential rational zeros of the following function.  Please show all work b/c I am not understanding this.
f(x)=7x^4-x^2+3

mertsj · Answer

The possible rational roots are the factors of the constant term (which in this case is 3) divided by the factors of the coefficient of the leading term (which in this case is 7).
So the possible rational roots are:
$$\frac{\pm1,\pm3}{\pm1,\pm7}$$

mertsj · Answer

You can then use synthetic division to see if any of them are actual roots.

anonymous · Answer

what do u mean

mertsj · Answer

do you know synthetic division?

mertsj · Answer

I can do an example.  Perhaps it will jog your memory.

mertsj · Answer

Oh.  Perhaps you have not yet learned it because the problem says to list the possible rational zeros.  They are as I have indicated.  Do you want a complete list?

mertsj · Answer

$$\pm1,\pm3,\pm\frac{1}{7},\pm\frac{3}{7}$$

anonymous · Answer

so do i divide them, put them into an equation or what?

mertsj · Answer

I think you are done.  The problem only asked you for the possibilities.

anonymous · Answer

oh ok

mertsj · Answer

I think after you master this your next lesson might be to see whether any of the possibilities are actual roots.  Then you will probably learn synthetic division and some other techniques for finding roots of polynomial equations.