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If x is real, the expression $\frac{x + 2}{2 x^{2} + 3 x + 6}$ takes all value in the interval

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(113,13)

[-113, 13]

(-13, 113)

None of these

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detailed solution

Correct option is B

If the given expression be y, theny=2x2y+(3y-1)x+(6y-2)=0If y≠0 then ∆≥0 for real x i.e., B2-4AC≥0or -39 y2+10y+1≥0 or (13y+1(3y-1)≤0⇒-1/13≤y≤1/3If y=0 then x=-2 which is real and this value of y is included in the above range.

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If x is real, the expression x+22x2+3x+6 takes all value in the interval

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If x is real, the expression $\frac{x + 2}{2 x^{2} + 3 x + 6}$ takes all value in the interval