Question

If `x` is real, then the value of the expression `(x^2+14 x+9)/(x^2+2x+3)` lies between (a) 5 and 4 (b) 5 and `-4` (c) `-5a n d4` (d) none of these
A. [4, 5]
B. [-4, 5]
C. [-5, 4]
D. none of these

Answer 1

Correct Answer - C
`(x^(2)+14x+9)/(x^(2)+2x+3)=y`
or ` x^(2)+14x+9=x^(2)y+2xy+3y`
or ` x^(2)(y-1)+2x(y-7)+(3y-9)=0`
Since x is real, we have
`4(y-7)^(2)-4(3y-9)(y-1) ge 0`
or ` 4(y^(2)+49-14y)-4(3y^(2)+9-12y) ge 0`
or ` (y+5)(y-4) le 0`
` :. y in [-5,4]`