distinct roots in quadratic and quartic
Source: Russia 1994
October 6, 2008
quadraticsalgebra unsolvedalgebra
Problem Statement
The equation x^2 \plus{} ax \plus{} b \equal{} 0 has two distinct real roots. Prove that the equation x^4 \plus{} ax^3 \plus{} (b \minus{} 2)x^2 \minus{} ax \plus{} 1 \equal{} 0 has four distinct real roots.