If `alpha,beta` are the roots of the equation `a x^2+b x+c=0,` then find the roots of the equation `a x^2-b x(x-1)+c(x-1)^2=0` in term of `alphaa n dbetadot`

Explanation

`ax^(2) - bx (x - 1) + c (x -1)^(2) = 0`
`rArr (ax)/((1-x)^(20)) + (bx)/( 1- x) + c = 0` (1)
Now , `alpha` is a root of `ax^(2) +bx + c = 0 `. Then let
`alpha = (x) /(1-x)`
`rArr x = (alpha)/(alpha + 1)`
Hence, the roots of (1) are `alpha //(1 + alpha ),beta//(1 + beta)`.