Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c) (x -a) =0 are always real and these cannot be equal unless a=b=c

Prove that both the roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-a)(x-c)=0 are real.

Both the roots of the equation : (x - b) (x -c) + (x - c) (x - a) + (x - a) (x - b) = 0 are always :

If the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are equal then

If the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are equal then

IF a,b,c are real, prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real and cannot be equal unless a=b=c.

show that the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 where a,b,c in R are always real.Find the condition that the roots may be equal.what are the roots when this condition satisfied.