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Question

If x is real, the expression x+22x2+3x+6 takes all value in the interval
  1. (13,13)
  2. (113,13)
  3. [113,13]
  4. None of these


Solution

The correct option is C [113,13]

If the given expression be y, then 2x2y+(3y1)x+(6y2)=0
If y0 then 0 for real x i.e., b24ac0
or 39y2+10y+10 or (13y+1)(3y1)0
113y13
If y=0 the x=2 which is real and this value of y is included in the above range.

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