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AP EAMCET2011MathematicsFunctions

If x is real, then the value of x^2-3 x+4 x^2+3 x+4 lies in the interval

Options

  1. A[ 1 3 , 3 ]
  2. B[ 1 5 , 5 ]
  3. C[ 1 6 , 6 ]
  4. D[ 1 7 , 7 ]

Correct answer

D. [ 1 7 , 7 ]

Step-by-step solution

aligned & Let y= x^2-3 x+4 x^2+3 x+4 & x^2(y-1)+x(3 y+3)+(4 y-4)=0 aligned Since, x is real. array lc & D 0 & B^2-4 A C 0 & (3 y+3)^2-4(y-1)(4 y-4) 0 & 9 y^2+9+18 y-16 (y^2+1-2 y ) 0 & 7 y^2-50 y+7 0 & (7 y-1)(y-7) 0 & 1 7 y 7 array

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