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AP EAMCET201822 Apr 2018Evening ShiftMathematicsQuadratic EquationActual

f(x) is a quadratic expression such that f(x) is negative when x (- ,- 5 3 ) (3, ) and positive when x (- 5 3 , 3 ) g(x) is another quadratic expression such that g(x) is negative when x (3, 9 2 ) and positive when x R- [3, 9 2 ] . Then, the sign of f(x) g(x) in [0,5] is

Options

  1. Apositive in [0, 9 2 ] and negative in ( 9 2 , 5 )
  2. Bpositive in [0,3) (3, 9 2 ) and negative in ( 9 2 , 5 ]
  3. Cpositive in [0,3) (3, 9 2 ) ( 9 2 , 5 ]
  4. Dnegative in [0,3) (3, 9 2 ) ( 9 2 , 5 ]

Correct answer

B. positive in [0,3) (3, 9 2 ) and negative in ( 9 2 , 5 ]

Step-by-step solution

f(x)=a (x+ 5 3 )(3-x), a>0 and g(x)=b(x-3) (x- 9 2 ), b>0 Now, f(x) g(x)=a b (x+ 5 3 )(3-x)(x-3) (x- 9 2 ) According to wavy curve method, So, f(x) g(x) is positive in [0,3) (3, 9 2 ) and negative in ( 9 2 , 5 ) .

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