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 equal to the sum of the squares of their reciprocals,then prove that 2a^2c=c^2b+b^2a .

The sum of the roots of the quadratic equations ax^(2) + bx + c=0 is

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 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 equation a x^(2)+b x+c=0 is equal to the sum of the squares of their reciprocals, then

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 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 quadratic equation a x^2+b x+c=0 is equal to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.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, then a/c, b/a and c/b are in