If $α$ , $β$ are the roots of $3 x^{2} - 4 x + 1 = 0$ the equation whose roots are $\frac{α}{β}, \frac{β}{α}$ is?

3 x^{2} + 10 x + 3 = 0

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3 x^{2} + 10 x - 3 = 0

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3 x^{2} - 10 x - 3 = 0

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3 x^{2} - 10 x + 3 = 0

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Solution

The correct option is C $3 x^{2} - 10 x + 3 = 0$
$α$ , $β$ are the roots of $3 x^{2} - 4 x + 1 = 0$
$α = 1, β = \frac{1}{3}$
Hence, $\frac{α}{β} = \frac{1}{3} a n d \frac{α}{β} = 3$
therefore sum of roots $\frac{α}{β} + \frac{α}{β} = \frac{10}{3}$
Product of roots, $(\frac{α}{β}) (\frac{β}{α}) = 1$
Therefore, equation will be, $x^{2} - \frac{10}{3} x + 1 = 0$
$3 x^{2} - 10 x + 3 = 0$

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