If $α, β$ are the roots of $x^{2} + 6 x + 9 = 0$ , then the equation whose roots are $\frac{1}{α}, \frac{1}{β}$ is

2 x^{2} + 3 x + 18 = 0

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x^{2} + 6 x - 9 = 0

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9 x^{2} + 6 x + 1 = 0

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9 x^{2} - 6 x + 1 = 0

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Solution

The correct option is C $9 x^{2} + 6 x + 1 = 0$
$α, β$ are roots of equation
$x^{2} + 6 x + 9 = 0$
$α + β = - 6$ & $α β = 9$
So, if roots are $\frac{1}{α}, \frac{1}{β}$
$x^{2} - (\frac{1}{α} + \frac{1}{β}) x + \frac{1}{α β} = 0$
$x^{2} - (\frac{α + β}{α β}) x + \frac{1}{α β} = 0$
$x^{2} + \frac{6}{9} x + \frac{1}{9} = 0$
$9 x^{2} + 6 x + 1 = 0$ -Answer

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