Question

How do you use the rational root theorem to find the roots of `x^4 – 7x^2 + 12 = 0`?

Answer 1

Evaluation of `x^4-x^2+12` for all factors of `12`
gives the roots `x=2` and `x=-2`

Explanation:

According to the Rational Root Theorem in its simplified form
when `f(x)`is a monic polynomial (a polynomial whose highest degree term has a coefficient of `1`)
if `a` is a rational root of `f(x)` then `a` must be a factor of the constant term of `f(x)`

For the given example, this means that any rational root of `x^4-7x^2+12` but be a factor of `12`.

The factors of `12` are `{1,2,3,4,6,-1,-2,-3,-4,-6}`

We can test each of these factors (as I did with Excel, below) to find all rational roots of `f(x)`