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.

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

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

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

Find the roots of the quadratic equation: a^(2)b^(2)x^(2)+b^(2)x-a^(2)x-1=0

If a,b,c are positive rational numbers such that agtbgtc and the quadratic eqution (a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 has a root of the interval (-1,0) then (A) c+alt2b (B) the roots of the equation are rational (C) the roots of are imaginary (D) none of these