If $\alpha$ and $\beta$ are the roots of $a x^2+b x+c=0$, then the roots of $a x^2-b x(x-1)+c(x-1)^2=0$ are

• A

  $\frac{\alpha+1}{\alpha}, \frac{\beta+1}{\beta}$
• Correct answer
  B

  $\frac{\alpha}{\alpha+1}, \frac{\beta}{\beta+1}$
• C

  $\frac{\alpha}{\beta}, \frac{\beta}{\alpha}$
• D

  $\frac{\alpha-1}{\alpha+1}, \frac{\beta-1}{\beta+1}$

Hence, the correct answer is option: 'B'.