Let $(\alpha, \beta)$ be the centroid of the triangle formed by the lines $15 x-y=82,6 x-5 y=-4$ and $9 x+4 y=17$. Then $\alpha+2 \beta$ and $2 \alpha-\beta$ are the roots of the equation :

Question

$x^{2}-7 x+12=0$

$x^{2}-13 x+42=0$

$x^{2}-14 x+48=0$

$x^{2}-10 x+25=0$

Solution

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