2
$\begingroup$

If a polynomial has only integer roots, is it always possible to find a root using the rational roots theorem?

  • 2
    It's difficult to answer till you clarify precisely what you mean by "find a root". E.g. it could mean anything ranging from a nonconstructive existence proof to a polynomial time root-finding algorithm.2011-12-20

1 Answers 1

1

if $a_nx^n+\cdots+a_0\in\mathbb{Z}[x]$ then every rational root is in the set $\{c/d : c|a_0, d|a_n\}$ as one can see by plugging in $c/d$ and multiplying the whole expression by $d^n$

  • 0
    @BillDubuque does it work when there are two variables?2012-09-01