If a,b and c are real numbers then the roots of the equation `(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0` are always

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

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

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

If a, b and c are distinct real numbers, prove that the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has real and distinct roots.

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, then both the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are always (A) positive (B) negative (C) real (D) imaginary.