JEE Advance - Mathematics (2007 - No. 20)
Let $$\alpha ,\,\beta $$ be the roots of the equation $${x^2} - px + r = 0$$ and $${\alpha \over 2},\,2\beta $$ be the roots of the equation $${x^2} - qx + r = 0$$. Then the value of $$r$$
$${2 \over 9}\left( {p - q} \right)\left( {2q - p} \right)$$
$${2 \over 9}\left( {q - p} \right)\left( {2p - q} \right)$$
$${2 \over 9}\left( {q - 2p} \right)\left( {2q - p} \right)$$
$${2 \over 9}\left( {2p - q} \right)\left( {2q - p} \right)$$