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

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Solution

Consider $f (x) = 3 x^{2} + 5 x - 2 = 0$

$∴$ Required equation $f (\frac{1}{x}) = 3 {(\frac{1}{x})}^{2} + 5 (\frac{1}{x}) - 2 = 0$

$\Rightarrow \frac{3}{x^{2}} + \frac{5}{x} - 2 = 0$

$\Rightarrow 3 + 5 x - 2 x^{2} = 0$

$\Rightarrow 2 x^{2} - 5 x - 3 = 0$

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