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

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

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

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

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

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Solution

The correct option is C $3 x^{2} + 5 x + 2 = 0$
The quadratic equation whose roots are reciprocal of $2 x^{2} + 5 x + 3 = 0$ can be obtained by replacing $x$ by $\frac{1}{x}$ .
Hence, $2 (\frac{1}{x})^{2} + 5 \frac{1}{x} + 3 = 0$
$3 x^{2} + 5 x + 2 = 0$

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