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JEE Main202313 Apr 2023Evening ShiftMathematicsStraight LinesActual

Let ( α , β ) 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 α + 2 β and 2 α - β are the roots of the equation

Options

  1. Ax 2 - 7 x + 12 = 0
  2. Bx 2 - 14 x + 48 = 0
  3. Cx 2 - 13 x + 42 = 0
  4. Dx 2 - 10 x + 25 = 0

Correct answer

C. x 2 - 13 x + 42 = 0

Step-by-step solution

The given set of equations are: 15 x - y = 82 6 x - 5 y = - 4 9 x + 4 y = 17 Now on solving the above equation by taking two at a time and plotting the diagram we get, ( α , β ) ≡ 1 + 5 + 6 3 , 2 - 7 + 8 3 ≡ ( 4 , 1 ) Hence, α + 2 β = 6 and 2 α - β = 7 The required equation is x - 6 x - 7 = 0 Equation x 2 - 13 x + 42 = 0 Hence this is the required option.

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