Suppose a, b, c are three non-zero real numbers. The equationx2+(a+b+c)x+a2+b2+c2=0has

Discriminant D of (1) is given byD=(a+b+c)2−4a2+b2+c2=−b2+c2−2bc+c2+a2−2ca+a2+b2−2ab)+a2+b2+c2=−(b−c)2+(c−a)2+(a−b)2+a2+b2+c2<0Thus, (1) cannot have real roots.