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

If the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

Show that the roots of the quadratic equation: (b - c)x^(2) + (c - a) x + (a - b) = 0 are equal if c + a = 2b.

If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are real and equal then prove that 2b=a+c.

Find the roots of quadratic equation ax^(2) + (a-b + c) x - b +c = 0 .

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

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

If the roots of the quadratic equation a(b-c)x^2+b(c-a)+c(a-b)=0 be equal then prove that a,b,c are in Harmonic progression .

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are,when ab+bc+ca=0