Quadratic EquationHard
Question
If $\alpha$ and $\beta$ are roots of the equation $ax^{2} + bx + c = 0$, then the roots of the equation ${ax}^{2} - bx(x + 1) + c(x + 1)^{2} = 0$ are
Options
A.$\frac{\alpha}{\alpha + 1},\frac{\beta}{\beta + 1}$
B.$\frac{- \alpha}{\alpha + 1},\frac{- \beta}{\beta + 1}$
C.$\frac{\alpha}{1 - \alpha},\frac{\beta}{1 - \beta}$
D.$\frac{\alpha}{\alpha - 1},\frac{\beta}{\beta - 1}$
Solution
$a\left( \frac{- x}{x + 1} \right)^{2} + b\left( \frac{- x}{x + 1} \right) + c = 0$
$$\Rightarrow \ \frac{- x}{x + 1} = \alpha,\beta \Rightarrow x = \frac{- \alpha}{\alpha + 1},\frac{- \beta}{\beta + 1}$$
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