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  • Let be the centroid of the triangle formed by the lines <img alt="15 x-y=82,6 x-5 y=-

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

Option: 1

x^2-13 x+42=0


Option: 2

x^2-10 x+25=0


Option: 3

x^2-7 x+12=0


Option: 4

x^2-14 x+48=0


Answers (1)

best_answer

$$ \begin{aligned} & \text { Centroid }(\alpha, \beta)=\left(\frac{6+1+5}{3}, \frac{8-7+2}{3}\right)=(4,1) \\ & \alpha+2 \beta=4+2=6 \\ & 2 \alpha-\beta=8-1=7 \end{aligned}

Quadratic \, \, equation\\ $$ \begin{aligned} & x^2-(6+7) x+(6 \times 7)=0 \\ & \Rightarrow x^2-13 x+42=0 \end{aligned}

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Suraj Bhandari

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