Find all possible rational roots using the rational root theorem.

x^4 - 3x^2 + 12 = 0

Plus/minus 1, 2, 3, 4, 6, 12?

It is a 4th degree equation, so at most you could have 4 roots

How can you possible get 6 of them ?

These are just possible rational roots, not the actual ones.

All I did was p/q.

The question was to "find all possible roots"

so you would try
f(1), f(-1) , f(2) ...., f(±12)
so you must try all of these

unfortunately, none are equal to zero, so you have no rational roots.

To find the possible rational roots of the given polynomial using the rational root theorem, we need to consider all the factors of the constant term (12) and divide them by the factors of the leading coefficient (1), including both positive and negative values.

In this case, the constant term is positive, so the signs of the possible rational roots are either positive or negative. The leading coefficient is already positive, so we don't need to consider its negative factors.

The factors of 12 are 1, 2, 3, 4, 6, and 12. Dividing each of these factors by 1 (the factors of the leading coefficient) gives us the following possible rational roots: ±1, ±2, ±3, ±4, ±6, and ±12.

Therefore, the possible rational roots of the given polynomial are: ±1, ±2, ±3, ±4, ±6, and ±12.