# How do you use the rational root theorem to find the roots of #x^3-9x^2+14x=48#?

##### 1 Answer

Test all possible values of

Any that satisfy the equation are roots of the equation.

#### Explanation:

The candidates for rational roots of

(notice, I've slightly re-arranged the equation)

are

Therefore there are

(It is useful if you can set this up as a spreadsheet or computer program.)

Here are the evaluations (using synthetic substitution/division) for the first

This gives us

Not of the subsequent factors gave a result of

It might be noted that treating these entries as synthetic division gives:

and taking the discriminant of