Question

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

Solution

## The correct option is C [−113,13]If the given expression be y, then 2x2y+(3y−1)x+(6y−2)=0 If y≠0 then △≥0 for real x i.e., b2−4ac≥0 or −39y2+10y+1≥0 or (13y+1)(3y−1)≤0 ⇒−113≤y≤13 If y=0 the x=−2 which is real and this value of y is included in the above range.

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