How do you use the rational root theorem to find the roots of x^3+2x-9=0?

1 Answer
Sep 22, 2015

The rational root theorem will only tell you what the possible rational roots are. This cubic has no rational roots.

Explanation:

By the rational root theorem, any rational root of x^3+2x-9=0 will be expressible in the form p/q in lowest terms, where p, q in ZZ, q != 0, p a divisor of the constant term 9 and q a divisor of the coefficient 1 of the leading term.

So the possible rational roots are:

+-1, +-3, +-9

None of these work.

Using Cardano's method, I found one Real root:

x = root(3)((81+sqrt(6657))/18) + root(3)((81-sqrt(6657))/18) ~~ 1.762496