if the ratio of the roots of the equation ax²+bx+c=0 m:n then​

Step-by-step explanation:

Let α,β be the roots of ax2+bx+c=0

Then, αβ=ac and α+β=a−b

Now it is given that,

βα=nm

Consider,

nm+mn

=βα+αβ

=α.βα2+β2

=α.β(α+β)2−2α.β

=aca2b2−ac

=acb2−ac