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.

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

If a,b,c are in A.P. then :

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

If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove that : 1/a,1/b,1/c are also in A.P.

If a, b,c be the sides of a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=90 are equal then sin^2 A/2, sin^2 B/2, sin^2 C/2 are in

If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,c are in A.P.

Which one of the following is one of the roots of the equation (b-c) x^2 + (c-a)x+(a-b)=0 ?

If a, b, c are real, then both the roots of the equation : (x- b) (x-c) + (x-c) (x-a) + (x-a)(x-b) are always :

If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P, prove that a, b, c are in A.P.

If the sum of the roots of ax^2bx +c = 0 is equal to the sum of the squares of their reciprocals, then show that c/a, a/b, b/c are in A.P.