If the roots of the equation ax2+bx+c=0 and where a≠0 and c≠0 and α and β then the equation whose roots are 1/α2 and 1/β2 is

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If the roots of the equation $a x^{2} + b x + c = 0$ and where $a \neq 0$ and $c \neq 0$ and $α$ and $β$ then the equation whose roots are $1 / α^{2}$ and $1 / β^{2}$ is

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

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

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

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

answer is A.

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Detailed Solution

$\begin{array}{l} α, β are roots of a x^{2} + b x + c = 0 \\ \Rightarrow α + β = - b / a, α β = c / a \end{array}$
$the equation whose roots are \frac{1}{α^{2}}, \frac{1}{β^{2}} is$
$\begin{array}{l} x^{2} - x (\frac{1}{α^{2}} + \frac{1}{β^{2}}) + \frac{1}{α^{2} β^{2}} = 0 \\ x^{2} - x (\frac{α^{2} + β^{2}}{(α β)^{2}}) + \frac{1}{(α β)^{2}} = 0 \\ \Rightarrow (α β)^{2} x^{2} - x (α + β)^{2} - 2 α β) + 1 = 0 \end{array}$
$\begin{aligned} \begin{array}{r} \Rightarrow \frac{c^{2}}{a^{2}} x^{2} - x (\frac{b^{2}}{a^{2}} - \frac{2 c}{a}) + 1 = 0 \\ \Rightarrow c^{2} x^{2} - x (b^{2} - 2 a c) + a^{2} = 0 \end{array} \end{aligned}$