If `a (b - c) x^2 + b (c-a) x + c (a - b) = 0` has equal root, then `a, b, c` are in

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

If the roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 are equal show that 1/a,1/b,1/c are in A.P.

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 equation (b-c)x^(2)+(c-a)x+(a-b)=0 are equal then a,b,c will be in