If the roots of the equation a(b-c) x^2+b(c-a) x+c(a-b)=0 are equal, then which one of the following is correct?

Step-by-step solution

a(b-c) x^2+b(c-a) x+c(a-b)=0 has coefficients in cyclic order its one root will be 1 . both the roots are equal other root =1 aligned & Product of roots =1 & c(a-b) a(b-c) =1 & a c-b c=a b-a c & 2 a c=a b+b c & 2 b = 1 a + 1 c & a, b, c are in HP. aligned