If x is real- the expression x-2-2 x2-3 x-6 takes all value in the intervalA- 1-13- 1-3B- -1-3- 1-13C- -1-13- 1-3-5 -1-3- 1-13-

The correct option is C If the given expression be y, then y = 2x^2y+(3y 1)x+(6y 2)=0 If y nbsp;≠ 0 then nbsp; Δ nbsp;≥ 0 for real x i.e. B^2 4AC≥0 or ...

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Standard XI

Mathematics

Definition of Functions

If x is real,...

Question

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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$\left [-\frac{1}{3}, \frac{1}{13} \right ]$

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Solution

The correct option is B

If the given expression be y, then

$y = 2 x^{2} y + (3 y - 1) x + (6 y - 2) = 0$

If y ≠ 0 then Δ ≥ 0 for real x i.e. $B^{2} - 4 A C \geq 0$

or $- 39 y^{2} + 10 y + 1 \geq 0 o r (13 y + 1) (3 y - 1) \leq 0$

⇒ $- \frac{1}{13} \leq y \leq \frac{1}{3}$

if y = 0 then x = -2 which is real and this value of y is included in the above range.

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Similar questions

Q. If x is real, the expression

\frac{x + 2}{2 x^{2} + 3 x + 6}

takes all value in the interval

Q. If x is real, the expression

\frac{x + 2}{(2 x^{2} + 3 x + 6)}

takes all value in the interval

Find

(a)

(b)

(c)

Q. The common difference of the A.P.

\frac{1}{3}, \frac{1 - 3 b}{3}, \frac{1 - 6 b}{3}, . . .

is

(a)

\frac{1}{3}

(b)

- \frac{1}{3}

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

The correct option is B If the given expression be y, then y=2x2y+(3y−1)x+(6y−2)=0 If y ≠ 0 then Δ ≥ 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 then x = -2 which is real and this value of y is included in the above range.

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