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BITSAT2024MathematicsTrigonometric Ratios & IdentitiesActual

The sum of all values of x in [0,2 ] , for which x+ 2 x+ 3 x+ 4 x=0 , is equal to :

Options

  1. A8
  2. B11
  3. C12
  4. D9

Correct answer

D. 9

Step-by-step solution

( x+ 4 x)+( 2 x+ 3 x)=0 2 5 x 2 3 x 2 +2 5 x 2 x 2 =0 2 5 x 2 3 x 2 + x 2 =0 2 5 x 2 2 x x 2 =02 5 x 2 =0 5 x 2 =0, , 2 , 3 , 4 , 5 , x=0, 2 5 , 4 5 , 6 5 , 8 5 , 2 x 2 =0 x 2 = 2 x= ; x=0 x= 2 , 3 2 So, sum =6 + +2 =9

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