Problem:
The polynomial has three roots in the complex plane. What is the area of the triangle formed by these roots?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let . Then the polynomial becomes . We spot that is a root of this polynomial:
The three solutions for are then . Since shifting the solution back to is a translation of the points, we can just compute the area directly. Treating the segment between and as the base and as the vertex from which we drop the height, we see the area is .
The problems on this page are the property of the MAA's American Mathematics Competitions