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MHT CET202527 Apr 2025Evening ShiftMathematicsTrigonometric EquationsActual

The number of values of x in interval [0,5 ] satisfying the equation 3 ^2 x-7 x+2=0 is

Options

  1. A0
  2. B5
  3. C4
  4. D6

Correct answer

A. 0

Step-by-step solution

Treating the equation 3 ^2 x - 7 x + 2 = 0 as quadratic in x yields solutions x = 1 3 and x = 2 . The latter has no real solutions since 2 [-1,1] . For x = 1 3 , let = ( 1 3 ) (0, 2 ) . The general solution is x = n + (-1)^n for integer n . From n=0 to n=5 , the values , - , 2 + , 3 - , 4 + , and 5 - all lie within [0,5 ] . For n 6 , the values exceed 5 . Final answer: 6

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