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MHT CET202616 April 2026Morning ShiftMathematicsTrigonometric EquationsActual

If 0 x 2 , then the number of values of x for which x - 2x + 3x = 0 is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

The given equation is x - 2x + 3x = 0 Grouping the terms, we get ( 3x + x) - 2x = 0 Using the formula C + D = 2 ( C+D 2 ) ( C-D 2 ) , we have: 2 2x x - 2x = 0 2x (2 x - 1) = 0 This gives 2x = 0 or x = 1 2 For 2x = 0 , since 0 x 2 , we have 0 2x . Thus, 2x = 0 or 2x = , which gives x = 0 or x = 2 . For x = 1 2 , since 0 x 2 , we get x = 3 . The possible values of x are 0, 3 , 2 . Therefore, the number of values of x is 3 . Answer: 3

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