Complex Numbers And Quadratic Equations question 13
Question: If x is real, the expression $ \frac{x+2}{2x^{2}+3x+6} $ takes all value in the interval [IIT 1969]
Options:
A) $ ( \frac{1}{13},\frac{1}{3} ) $
B) $ [ -\frac{1}{13},\frac{1}{3} ] $
C) $ ( -\frac{1}{3},\frac{1}{13} ) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
If the given expression be y, then $ y=2x^{2}y+(3y-1)x+(6y-2)=0 $ If $ y\ne 0 $ then $ \Delta \ge 0 $ for real x i.e. $ B^{2}-4AC\ge 0 $ or - $ 39y^{2}+10y+1\ge 0 $ or $ (13y+1)(3y-1)\le 0 $
Þ $ -1/13\le y\le 1/3 $ If $ y=0 $ then $ x=-2 $ which is real and this value of $ y $ is included in the above range.
BETA
