Question

How do you use the rational root theorem to list all possible roots for `x^3+81x^2-49x-49=0`?

Answer 1

The list of all possible rational roots is `+-1,+-7.+-49`

Explanation:

`color(blue)1x^3+81x^2-49x-color(red)(49)=0`

The rational roots theorem says that the list of POSSIBLE rational roots is the factors of the constant `color(red)(49)` divided by the factors of the leading coefficient `color(blue)1`.

The factors of the constant are known as `color(red)p` and the factors of the leading coefficient are known as `color(blue)q`.

`color(red)p/color(blue)q=frac{+-1,+-7,+-49}{+-1}=+-1,+-7,+-49`