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JEE Main202623 January 2026Morning ShiftMathematicsQuadratic EquationActual

If and ( < ) are the roots of the equation (-2+ 3 )(| x -3|)+(x-6 x )+(9-2 3 )=0, x 0 , then + is equal to :

Options

  1. A8
  2. B11
  3. C9
  4. D10

Correct answer

D. 10

Step-by-step solution

Let t = x 0 . The equation becomes (-2+ 3 )|t-3| + (t^2 - 6t) + (9 - 2 3 ) = 0 . Since t^2 - 6t + 9 = (t-3)^2 , we get (t-3)^2 + ( 3 -2)|t-3| - 2 3 = 0 . Let u = |t-3| 0 : u^2 + ( 3 -2)u - 2 3 = 0 . Discriminant = ( 3 -2)^2 + 8 3 = 7 + 4 3 = (2+ 3 )^2 . u = (2- 3 ) (2+ 3 ) 2 , giving u = 2 or u = - 3 (rejected). |t-3| = 2 t = 5 or t = 1 , so x = 25 or x = 1 . = 1, = 25 . / + = 25 + 25 = 5 + 5 = 10 .

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