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If $x_{1}, x_{2}$ are roots of the equation $x^{2} - 5 x - 6 = 0$ then the equation whose roots are $2 x_{1} + 5, 2 x_{2} + 5$ is

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$x^{2} + 4 = 0$

$x^{2} - 51 = 0$

$x^{2} - 18 x + 32 = 0$

$x^{2} - 20 x + 51 = 0$

answer is D.

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Detailed Solution

$x_{1} = 6, x_{2} = - 1$
$∴$ New roots are = 17,3
$\Rightarrow$ equation is $x^{2} - 20 x + 51 = 0$

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