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If the equations $x^{2} - x - p = 0 and x^{2} + 2 p x - 12 = 0$ have a common root then that root is

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Cannot be determined

$p + 2$

answer is C.

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Detailed Solution

${(c_{1} a_{2} - c_{2} a_{1})}^{2} = (b_{1} c_{2} - b_{2} c_{1}) (a_{1} b_{2} - a_{2} b_{1})$

$\Rightarrow {(- p + 12)}^{2} = (12 + 2 p^{2}) (2 p + 1)$

$\Rightarrow 4 p^{3} + p^{2} + 48 p - 132 = 0$

$p = 2, ∴ the common root is 2$

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