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

1 Answer
George C.
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#

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