It is given that A,B,C and D are roots of the quartic equation X^4 - X +2 = 0. Determine, whether or not (AB+CD) is a root of the equation X^3 – 8X –1 = 0.

My roots for the quartic are gruesome algebraic expressions with approximate values

{-0.85-1.01 ä,-0.85+1.01 ä,0.85-0.65 ä,0.85+0.65 ä}

These are points on a circle centre -0.17.., radius 1.21...; but nothing more elegant.

Trying the various ab+cd permuations in f (x ) = x^3 - 8 x-1, I get results very close to zero for all.

 

Posted by goFish on 2005-12-22 20:20:42