If the sum of the roots of the quadratic equation `a x^2+b x+c=0` is equl 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 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 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 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 .

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 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

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

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 (a)/(c ), (b)/(a)" and "(c )/(b) are in

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.