Completing squares we can write the discriminant in the form
This implies for all i.e. all the roots are real. Besides, the roots are equal if and only if or equivalently if and only if .
Find the nature of roots for
(x-a)(x-b) + (x-c)(x-a) + (x-b)(x-c) = 0
I started solving the above equation.
This was deduced to
3x2 – 2(a + b+c)x +(ab+bc+ca) =0
from this, the discreminant
4(a + b+c)2 -4(3)( ab+bc+ca)
4[a2+b2+c2+2(ab+bc+ca)-3(ab+bc+ca)]
4[a2+b2+c2-(ab+bc+ca)]
From this I am not able to say what type are the roots.
Kindly guide me.
Thanks