INMO 1998 Problem 5

Suppose $a,b,c$ are three rela numbers such that the quadratic equation $$x^2 - (a +b +c )x + (ab +bc +ca) = 0$$ has roots of the form $\alpha + i \beta$ where $\alpha > 0$ and $\beta \not= 0$ are real numbers. Show that (i) The numbers $a,b,c$ are all positive. (ii) The numbers $\sqrt{a}, \sqrt{b} , \sqrt{c}$ form the sides of a triangle.