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If the roots of the quadratic equation $a x^{2} + b x + c = 0$ are $α, β$ then the roots of the quadratic equation
$a x^{2} - b x (x - 1) + c (x - 1)^{2} = 0$ are

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$1 - α, 1 - β$

$\frac{α + 1}{α}, \frac{β + 1}{β}$

$\frac{α}{α - 1}, \frac{β}{β - 1}$

$\frac{α}{α + 1}, \frac{β}{β + 1}$

answer is C.

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Detailed Solution

$a x^{2} - b x (x - 1) + c (x - 1)^{2} - 0$

$\begin{array}{l} \Rightarrow a {(- \frac{x}{x - 1})}^{2} + b (- \frac{x}{x - 1}) + c = 0 \\ \Rightarrow - \frac{x}{x - 1} = α, β \\ \Rightarrow x = \frac{α}{α + 1}, \frac{β}{β + 1} \end{array}$

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