$a,b,c$ are reals, such that every pair of equations of $x^3-ax^2+b=0,x^3-bx^2+c=0,x^3-cx^2+a=0$ has common root. Prove $a=b=c$
Source: St Petersburg Olympiad 2012, Grade 11, P1
Tags: algebra
$a,b,c$ are reals, such that every pair of equations of $x^3-ax^2+b=0,x^3-bx^2+c=0,x^3-cx^2+a=0$ has common root. Prove $a=b=c$