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AP EAMCET201923 Apr 2019Morning ShiftMathematicsFunctionsActual

If ( | x^2+k x+1 x^2+x+1 | < 3 ) for all real numbers (x ), then the range of the parameter (k ) is

Options

  1. A((0,4) )
  2. B((-1,5) )
  3. C((-4,0) )
  4. D((-5,1) )

Correct answer

B. ((-1,5) )

Step-by-step solution

It is given, for all (x R ) ( aligned & | x^2+k x+1 x^2+x+1 | 0, x R ] aligned ) So, (4 x^2+(k+3) x+4 > 0, x R ) Then (D 0, x R ) Then (D < 0 (3-k)^2-16 < 0 ) ( (k-3-4)(k-3+4) < 0 ) ( k (-1,7) (ii) ) From intervals (i) and (ii), we get (k (-1,5) ) Hence, option (b) is correct.

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