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Manipal MET2011MathematicsFunctions

If x is real, then the value of x^2+34 x-71 x^2+2 x-7 does not lie between

Options

  1. A8 and -5
  2. B0 and 9
  3. C-5 and 9
  4. D5 and 9

Correct answer

D. 5 and 9

Step-by-step solution

aligned & Let y= x^2+34 x-71 x^2+2 x-7 & x^2(y-1)+2(y-17) x+(71-7 y)=0 aligned For real values of x , its discriminant, D 0 4(y-17)^2-4(y-1)(71-7 y) 0 array ll & (y^2-34 y+289 ) & - (71 y-7 y^2-71+7 y ) 0 & y^2-14 y+45 0 & (y-5)(y-9) 0 & y 5 and y 9 array Hence, y does not lie between 5 and 9

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