Find the equation whose roots are the reciprocals of the roots of $3 x^{2} - 5 x + 7 = 0$

7 x^{2} - 5 x + 3 = 0

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7 x^{2} + 5 x + 3 = 0

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4 x^{2} - 5 x + 3 = 0

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7 x^{2} - 5 x + 7 = 0

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Solution

The correct option is B $7 x^{2} - 5 x + 3 = 0$
$α + β = \frac{- b}{a} = \frac{5}{3}$ & $α β = \frac{7}{3}$
Reciprocal roots are $\frac{1}{α}$ & $\frac{1}{β}$
$\Rightarrow \frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{5}{7}$ & $(\frac{1}{α} \frac{1}{β}) = \frac{3}{7}$
$\Rightarrow$ eq $^{n}$ is $x^{2} - (\frac{1}{α} + \frac{1}{β}) x + \frac{1}{α β} = 0$
$\Rightarrow x^{2} - \frac{5}{7} x + \frac{3}{7} = 0$
$\Rightarrow 7 x^{2} - 5 x + 3 = 0$

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