MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2014 Harvard-MIT Mathematics Tournament
8
2014 Algebra #8: True for Exactly One Value
2014 Algebra #8: True for Exactly One Value
Source:
July 7, 2014
symmetry
algebra
polynomial
inequalities
Problem Statement
Find all real numbers
k
k
k
such that
r
4
+
k
r
3
+
r
2
+
4
k
r
+
16
=
0
r^4+kr^3+r^2+4kr+16=0
r
4
+
k
r
3
+
r
2
+
4
k
r
+
16
=
0
is true for exactly one real number
r
r
r
.
Back to Problems
View on AoPS