Functions Question 658
Question: If x is real, then value of the expression $ \frac{x^{2}+14x+9}{x^{2}+2x+3} $ lies between
[UPSEAT 2002]
Options:
A) 5 and 4
B) 5 and ?4
C) ? 5 and 4
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{x^{2}+14x+9}{x^{2}+2x+3}=y $
Þ $ x^{2}+14x+9=x^{2}y+2xy+3y $
Þ $ x^{2}(y-1)+2x(y-7)+(3y-9)=0 $ Since x is real, \ $ 4{{(y-7)}^{2}}-4(3y-9)(y-1)>0 $
Þ $ 4(y^{2}+49-14y)-4(3y^{2}+9-12y)>0 $
Þ $ 4y^{2}+196-56y-12y^{2}-36+48y>0 $
Þ $ 8y^{2}+8y-160<0 $
Þ $ y^{2}+y-20<0 $
Þ $ (y+5)(y-4)<0 $ ; \ y lies between ? 5 and 4.
BETA
