Let A(x) = be the matrix
0 a-x b-x -a-x 0 c-x -b-x -c-x 0For which (a, b, c) does det A(x) = 0 have a repeated root in x?
Multiplying out, we find that det A(x) = -2x3 + 2(bc - ac + ab)x. This has roots 0 and ±√(ab + bc - ac). This has a repeated root iff ac = ab + bc.
12th Putnam 1952
© John Scholes
5 Mar 2002