19th Australian 1998 Problem A1 Find all the real roots of (x + 1998) (x + 1999) (x + 2000) (x + 2001) + 1 = 0.
x = -3999/2 ± ½ √5 Solution Put y = x 2 + 3999x + 1998·2001. Then the polynomial is y(y + 2) + 1 = (y + 1) 2 . Thanks to Vikash Rungta for sending this solution. 19th Aus 1998 © John Scholes jscholes@kalva.demon.co.uk 1 Mar 2003 Last updated/corrected 1 Mar 03