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AP EAMCET201923 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

If (a ) and (b ) are the maximum and minimum values of the quadratic expressions (1-2 x-5 x^2 ) and (x^2-2 x+5 ) respectively, then the set of all values of (x ) for which the expression (5 a x^2+b x+7 ) is positive, is

Options

  1. A((a, b) )
  2. B((- , 7) )
  3. C((5, ) )
  4. D((- , ) )

Correct answer

D. ((- , ) )

Step-by-step solution

The maximum value of the expression ( aligned & 1-2 x-5 x^2 & a=- 4+20 4(-5) = 6 5 aligned ) and minimum value of the expression (x^2-2 x+5 ), (b=- 4-20 4 =4 ) Now, the given quadratic expression (5 a x^2+b x+7 ) at (a= 6 5 ) and (b=4 ) must be positive, then (6 x^2+4 x+7 > 0 ) ( ) Discriminant (D=16-4(6)(7) 0, x R=(- , ) . ) Hence, option (d) is correct.

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