If `r` is the ratio of the roots of the equation `ax^2 + bx + c = 0` , show that `(r+1)^2/r =(b^2)/(ac)`

Explanation

`:' (alpha)/(beta)=r`
`implies (alpha+beta)/(alpha-beta)=(r+1)/(r-1)`
[using componendo and dividendo method]
`implies(-b//a)/((sqrt(D))/a)=(r+1)/(r-1)impliesb(1-4)=(1+r)sqrt(D)`
On squaring both sides we get
`implies b^(2)(1-r)^(2)=(1+r)^(2)(b^(2)-4ac)`
or `(1+r)^(2).4ac=b^(2)(4r)` or `((1+r)^(2))/4=(b^(2))/(ac)`