November 27–December 3, 2007

Problem

Consider the real polynomial

p(x) = 1 + a x + b x^2 + a x^3 + x^4

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.

Solution

here.

List of solvers

Aaron Dilley (undergraduate); Dustin Moody, Gary Raymond (graduate)

Gary Raymond wins the prize!