If the sum of the roots of the equation is equal to the sum of the squares of their reciprocals, then (A) `a,b,c` are in A.P. (B) `a^2,b^2,c^2` are in G.P. (C) `ab^2,bc^2,ca^2` are in A.P. (D) `ab,bc,ca` are G.P.

If the sum of the roots of the equation ax^2 +bx +c=0 is equal to sum of the squares of their reciprocals, then bc^2,ca^2 ,ab^2 are in

If sum of the roots of ax^(2)+bx+c=0 is equal to the sum of the squares of their reciprocals then show that 2a^(2)c=ab^(2)+bc^(2) .

The sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their recipocals, prove that (c)/(a),(a)/(b),(b)/(c) are in A.P.

In a /_\ABC, tan\ A/2 = 5/6 and tan\ C/2 = 2/5 then (A) a,c,b are in A.P. (B) a,b,c are in A.P. (C) b,a,c are in A.P. (D) a,b,c are in G.P.

If l n(a+c),l n(a-c) and l n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. (d) a ,b ,c are in H.P.

If bx+cy=a , there a, b, c are of the same sign, be a line such that the area enclosed by the line and the axes of reference is 1/8 square units, then : (A) b,a,c are in G.P. (B) b, 2a, c arein G.P. (C) b, a/2, c are in A.P. (D) b, -2a, c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d -c are in G.P.

Roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are real and equal, then (A) a+b+c!=0 (B) a,b,c are in H.P. (C) a,b,c are in A.P. (D) a,b,c are in G.P.