Question

show that if the roots of the equation (a^2+b^2)^2 x^2+2x(ac+bd)+c^2+d^2=0 are equal then a÷b=c÷d

Answer 1

The study of real valued roots are predictable for the value of the discriminant D to be ≥0.In this case D=√{B²-4AC}=√[{2(ac+bd)²-4(a²+b²)(c²+d²)}]=√4[(ac+bd)²-(a²+b²)(c²+d²)]

=(ac+bd)²-(a²+b²)(c²+d²)=a²c²+b²d²+2acbd-a²c²-a²d²-b²c²-b²d²=2abcd-a²d²-b²c²=-(ad-bc)²=>D≤0.But the predictable value of D is ≥0.Sosatisfying the two statements could imply D=0.For which the quadratic eqns is bound to have real equal root.
i hope it will help you

Answer 2

Question in not correctly given