1983 AIME Problems/Problem 3
Problem
What is the product of the real roots of the equation ?
Solution
If we expand this, we get a quartic polynomial, which obviously isn't very helpful.
Instead, we substitute for
and our equation becomes
.
Solving for , we get
or
. The second solution gives us non-real roots, so we'll will go with the first. Substituting
back in for
,
. The product of our roots is therefore 20.