Find the equation whose roots are reciprocals of the roots of $2 x^{2} + 5 x + 4 = 0$ .

$4 x^{2} + 2 x + 5 = 0$

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$5 x^{2} + 4 x + 2 = 0$

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$2 x^{2} + 4 x + 5 = 0$

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$4 x^{2} + 5 x + 2 = 0$

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Solution

The correct option is D
$4 x^{2} + 5 x + 2 = 0$

To get the equation whose roots are reciprocals, replace $x$ by $\frac{1}{x}$ .

$\Rightarrow 2 \times \frac{1}{x^{2}} + \frac{5}{x} + 4 = 0$

Multiplying by $x^{2}$ , ( $x \neq 0$ )

$\Rightarrow 2 + 5 x + 4 x^{2} = 0 o r 4 x^{2} + 5 x + 2 = 0$

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