November 27–December 3, 2007
Consider the real polynomial
Find the coefficients a and b that minimize the quantity a2 + b2 such that p(x) has at least one real root.
Hint: Since p(x) is palindromic it is possible to deal with a polynomial with half the degree by considering the quantity p(x)/x2 and making the substitution y = x + 1/x.
List of solvers
Aaron Dilley (undergraduate); Dustin Moody, Gary Raymond (graduate)
Gary Raymond wins the prize!