jee-main 2023 Q66

jee-main · India · session2_13apr_shift2 Straight Lines & Coordinate Geometry Triangle Properties and Special Points

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
(1) $x ^ { 2 } - 7 x + 12 = 0$
(2) $x ^ { 2 } - 14 x + 48 = 0$
(3) $x ^ { 2 } - 13 x + 42 = 0$
(4) $x ^ { 2 } - 10 x + 25 = 0$

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\\
(1) $x ^ { 2 } - 7 x + 12 = 0$\\
(2) $x ^ { 2 } - 14 x + 48 = 0$\\
(3) $x ^ { 2 } - 13 x + 42 = 0$\\
(4) $x ^ { 2 } - 10 x + 25 = 0$

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