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AP EAMCET202017 Sep 2020Morning ShiftMathematicsFunctionsActual

If ([a, b] ) is the range of the function ( x+2 2 x^2+3 x+6 ) for (x R ), then

Options

  1. A(a < 0, b < 0 )
  2. B(a 0 )
  3. C(a>0, b>0 )
  4. D(a>0, b < 0 )

Correct answer

B. (a 0 )

Step-by-step solution

([a, b] ) is range of ( x+2 2 x^2+3 x+6 ) and (x R ) Let (y= x+2 2 x^2+3 x+6 ) ( aligned & 2 y x^2+3 x y+6 y=x+2 & 2 y x^2+(3 y-1) x+6 y-2=0 & x R So, D 0 & (3 y-1)^2-4(6 y-2)(2 y) 0 & -39 y^2+10 y+1 0 & 39 y^2-10 y-1 0 & (3 y-1)(13 y+1) 0 y [- 1 13 , 1 3 ] aligned ) So, ( a=- 1 13 , b= 1 3 ) ( a 0 )

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