Suppose a,b,c are three rela numbers such that the quadratic equation x2−(a+b+c)x+(ab+bc+ca)=0 has roots of the form α+iβ where α>0 and β=0 are real numbers. Show that
(i) The numbers a,b,c are all positive.
(ii) The numbers a,b,c form the sides of a triangle. quadraticsalgebrapolynomialinequalitiessum of rootsarea of a triangle