How do you use the rational root theorem to find the roots of #2x^3 - 9x^2 - 11x +8 = 0#?

1 Answer
George C.
May 23, 2015

If #p/q# is a root of #2x^3-9x^2-11x+8=0# expressed in lowest terms, then #p# is a divisor of the constant term #8# and #q# is a divisor of the coefficient #2# of the highest order term.

So if this polynomial has rational roots, they must be one of the following:

#-8#, #-4#, #-2#, #-1#, #-1/2#, #1/2#, #1#, #2#, #4# or #8#.

Unfortunately, none of these is a root, so this cubic has no rational roots and the rational root theorem cannot help us find the roots it does have.

Related questions
See all questions in Rational Zeros
Impact of this question
2189 views around the world
You can reuse this answer
Creative Commons License