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

Show that 1 is a root of a(b-c)x^(2)+b(c-a)x+c(a-b)=0 . Hence show that if roots of this equation are equal then (1)/(a),(1)/(b),(1)/(c) are in A.P

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

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

If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

Let a(b - c)x^2 + b(c - a)x + c(a -b) = 0 has two equal roots. The true relation is _____

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

If (b-c)^(2), (c-a)^(2), (a-b)^(2) are in A.P. then prove that, (1)/(b-c), (1)/(c-a), (1)/(a-b) are also in A.P.

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.

If (b+c)/(a), (c+a)/(b), (a+b)/(c ) are in A.P. show that (1)/(a), (1)/(b), (1)/(c ) are also in A.P. (a+b+c != 0) .

Show that 1 is a root of a(b-c)x^2+b(c-a)x+c(a-b)=0 .Hence show that if roots of this equation are equal then 1/a,1/b,1/c are in A.P.