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Let \((\alpha, \beta)\) be the centroid of the triangle formed by the lines \(15 x-y=82,6 x-5 y=-4\) and \(9 x+4 y=17\).…

Q1

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

[JEE Main 2023, 13 Apr (Shift 2)]

a

\(x^2-7 x+12=0\)

b

\(x^2-13 x+42=0\)

c

\(x^2-14 x+48=0\)

d

\(x^2-10 x+25=0\)

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