If the sum of the roots of the quadratic equation `ax^(2)+bx+c=0` is equal the sum of the cubes of their reciprocals, then prove that `ab^(2)=3abc+c^(3)`.

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equal to the sum of the squares of their reciprocals,then prove that 2a^(2)c=c^(2)b+b^(2)a

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equl to the sum of the squares of their reciprocals,then prove that (a)/(c),(b)/(a) and (c)/(b) are in H.P.

If the sum of the roots of the quadratic equations ax^(2) + bx+c=0 is equal to the sum of the squares of their reciprocals, then be (b^2)/(ac) + (bc)/(a^2) =

If the sum of the roots of the equation ax^(2) + bx+ c = 0 is equal to the sum of their squares then

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equal to the sum of the square of their reciprocals,then (a)/(c),(b)/(a) and (c)/(b) are in

If the sum of the roots of the quadrati equation ax^(2)+bx+c=0 is cqual to the sum of the squares of their reciprocals.Show that be ca ab are in A.P.

If the sum of the roots of the quadratic equation ax^2+bx+c=0 is equal to the sum of the squares of their reciprocals, show that bc^2,ca^2,ab^2 are in Arithmetic Progression (AP). It is well known that if any three consecutive terms, form a sequence, are such ttiat the difference between any two consecutive terms is same' then they are in AP.