Question

If (x - a)(x - b) + (x - c)(x - a)+ (x - c)(x - b) = 0 then it's roots are:

Answer 1

Answer:

Step-by-step explanation:

3x squre - 2x[a+b+c]+(ab+bc+ca)=0

Let D be the discriminant

D=4(a+b+c)squre−12(ab+bc+ca)

=4[(a+b+c)squre−3(ab+bc+ca)]

=2[2a squre+2b squre+2c squre−2ab−2bc−2ca]

=2[(a−b)squre+(b−c)squre+(c−a)squre

If D=0, then

(a−b)squre+(b−c)squre+(c−a)squre=0

⇒a−b=0;b=c;c=a

or   a=b=c