Explanation

(c)
We have, $ax^{2} - bx(x - 1) + c(x - 1)^{2} = 0$ ...(i)
$\Rightarrow \ a\left( \ \frac{x}{1 - x} \right)^{2} + b\left( \ \frac{x}{1 - x} \right) + c = 0$
Also, $\alpha\ and\ \beta$ be the roots of $ax^{2} + bx + c = 0$.
$\therefore\ \alpha = \frac{x}{1 - x}$ and $\beta = \frac{x}{1 - x}$
$\Rightarrow x = \frac{\alpha}{\alpha + 1},\ x = \frac{\beta}{\beta + 1}$
Hence, $\frac{\alpha}{\alpha + 1}$ and $\frac{\beta}{\beta + 1}\$are the required roots.