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MHT CET202617 April 2026Morning ShiftMathematicsTrigonometric EquationsActual

If the equation 3 - ^2 = 1 4 and [0, ] , then the number of solutions is...

Options

  1. A0
  2. B2
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

Given equation: 3 - ^2 = 1 4 Using the identities 3 = 3 - 4 ^3 and ^2 = 1 - ^2 , we get: 3 - 4 ^3 - (1 - ^2 ) = 1 4 Multiplying by 4 and rearranging the terms: 12 - 16 ^3 - 4 + 4 ^2 = 1 16 ^3 - 4 ^2 - 12 + 5 = 0 Let = x . Since [0, ] , we must have x [0, 1] . The equation becomes: 16x^3 - 4x^2 - 12x + 5 = 0 By inspection, x = 1 2 is a root. Factoring out (2x - 1) : (2x - 1)(8x^2 + 2x - 5) = 0 The roots are x = 1 2 and the solutions to 8x^2 + 2x - 5 = 0 . Using the quadratic formula: x = -2 4 - 4(8)(-5) 16 = -2 164

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