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 a c , b a and c b are in

Step-by-step solution

a x^2+b x+c=0, + = -b a , = c a As for given condition, + = 1 ^2 + 1 ^2 + =- ^2+ ^2 ^2 ^2 - b a = b^2 a^2 - 2 c a c^2 a^2 On simplification 2 a^2 c=a b^2+b c^2 2 a b = c a + b c a b , b a , & c b are in H.P.