if ad not = bc then prove that the equation .(a^2 + b^2)x^2 +2(ac+bd)x +(c^2+d^2) =0 has no equal roots. [note ^ means power and next To^ is its power number). Created by gurpanth1. Math

For a quadratic equation ax^2 + bx + c, the roots are equal if and only if the discriminant is 0. The discriminant is defined as b^2 - 4ac for this case.In your case, the quadratic equation is {2(ac+bd)}^2 - 4(a^2+b^2)(c^2+d^2) = 4(a^2c^2 + b^2d^2 + 2abcd) - 4(a^2c^2 + b^2d^2 + a^2d^2 + b^2c^2) = -4{(ad)^2 + (bc)^2 - 2*ab*cd} = -4(ad+bc)^2 whcih is zero if and only if ad = bc.But since that isn't true, the discriminant is non-zero and the roots are unequal.