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.

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