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If the equations $k (6 x^{2} + 3) + r x + 2 x^{2} - 1 = 0$ and $6 k (2 x^{2} + 1) + p x + 4 x^{2} - 2 = 0$ have both roots common, then $2 r - p =$

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Detailed Solution

Hint: $a_{1} x^{2} + b_{1} x + c_{1} = 0, a_{2} x^{2} + b_{2} x + c_{2} = 0$ have both roots common
$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

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