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AP EAMCET201920 Apr 2019Evening ShiftMathematicsFunctionsActual

If x R , then the range of x x^2-5 x+9 is

Options

  1. A(- 1 11 , 1 )
  2. B(- , -1 11 ) (1, )
  3. C[ -1 11 , 1 ]
  4. D[-1, 1 11 ]

Correct answer

C. [ -1 11 , 1 ]

Step-by-step solution

aligned & Let x x^2-5 x+9 =y & y x^2-(5 y+1) x+9 y=0 & x R D 0 (5 y+1)^2-36 y^2 0 & 25 y^2+10 y+1-36 y^2 0 & 11 y^2-10 y-1 0 & 11 y^2-11 y+y-1 0 & (11 y+1)(y-1) 0 y [- 1 11 , 1 ] aligned Hence, option (c) is correct.

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