Question

List the possible rational roots of 2x^3 + 17x^2 + 23x - 42 = 0

My answer: the possible rational roots are {±1, ±2, ±3, ±6, ±7, ±14, ±21, ±42. ±1/2, ±3/2, ± 7/2, ±21/2}.

Correct?

Answer 1

yes, and guess what?
x = 1 works!

after a quick synthetic division I got
2x^3 + 17x^2 + 23x - 42 = 0
(x-1)(x^2 + 19x + 42) = 0

and that quadratic factors very nicely again.

Answer 2

Yes, this is what you get when you apply the Rational Roots theorem.

But your list is very long, so it is of little use. It is a bit like answering the question by saying that all possible rational roots are the members of Q (as the problem didn't specifically say to list all the roots that the Rational Roots theorem yields).

Answer 3

Incorrect