The equation whose roots are reciprocals of the roots of the $7 x^{2} - 19 x + 5 = 0$ is

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

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7 x^{2} - 19 x + 5 = 0

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5 x^{2} - 19 x + 7 = 0

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5 x^{2} - 7 x + 19 = 0

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Solution

The correct option is D $5 x^{2} - 19 x + 7 = 0$
To find the equation whose roots are reciprocal of other equation, put $f (\frac{1}{x}) = 0$

$\Rightarrow 7 (\frac{1}{x^{2}}) - 19 (\frac{1}{x}) + 5 = 0$

$\Rightarrow 5 x^{2} - 19 x + 7 = 0$

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