Problem :
Let $a,b,c$ be the sides of triangle. No two of them are equal and $\lambda\in\Re$. If the roots of the equation $x^2+2(a+b+c)x+3\lambda(ab+bc+ca)=0$ are real, then find the range of $\lambda$
My approach : Since the sides are all different can we assume a =1 ,b=2 , c =3 so that the given equation becomes $x^2 +12x +33 \lambda$
Since roots are real therefore $12^2 -4 \times 33 \lambda > 0$
Solving the inequality we get $\lambda < \frac{72}{61}$ Please suggest whether this is correct method or not Thanks