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-a)^2=0` in term of `alphaa n dbetadot`

Explanation

`:'ax^(2)-bx(x-1)+c(x-1)^(2)=0`……….i
`impliesa(x/(x-1))^(2)-b(x/(x-1))+c=0`
or `a(x/(1-x))^(2)+b(x/(1-x))+c=0`
Now `alpha, beta` are the roots of `ax^(2)+bx+c=0`
Then `alpha=x/(1-x)` and `beta=x/(1-x)`
`impliesx=(alpha)/(alpha+1)` and `x=(beta)/(beta+1)`
hence `(alpha)/(alpha+1),(beta)/(beta+1)`,are the roots of the Eq. (i).