Too Many Values
Find all rational numbers \(a\), \(b\) and \(c\) such that the equation \(x^3 + ax^2+bx+c = 0 \) has roots \(a\), \(b\) and \(c\).
Enter your answer as the sum of all solutions. For example, if \((a,b,c)\) are \((5,6,7)\) and \((3,4,8)\), then enter your answer as \( 5+6+7+3+4+8=33\).
Note: \(b,c\) cannot be simultaneously equal to \(0\).