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

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

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

Show that the roots of (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are real, and that they cannot be equal unless a=b=c.

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

6.The roots of the equation (a-b+c)x^(2)+4(a-b)x+(a-b-c)=0 are

-If a,b,c in R then prove that the roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=0 are always real cannot have roots if a=b=c

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

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.

A root of the equation (a+c)/(x+a)+(b+c)/(x+b)=(2(a+b+c))/(x+a+b) is