1971 Canadian MO Problems/Problem 4
Determine all real numbers such that the two polynomials and have at least one root in common.
Let this root be . Then we have
Now, if , then we're done, since this satisfies the problem's conditions. If , then we can divide both sides by to obtain . Substituting this value into the first polynomial gives
It is easy to see that this value works for the second polynomial as well.
Therefore the only possible values of are and . Q.E.D.