Question

If $x$ is real, then the value of the expression $\frac{x^2+34 x-71}{x^2+2 x-7}$ does not exist between -

• A. $-5$ and 9
• B. 5 and -9
• C. -5 and -9
• D. 5 and 9

Answer 1

Answer: (D)

$\frac{x^2+34 x-71}{x^2+2 x-7}=y$
$x^2(1-y)+x(34-2 y)-71+7 y=0$
$x \in R D \geq 0$
$4(17-y)^2-(7 y-71)(1-y) \geq 0$
$(17-y)^2-\left[7 y-7 y^2-71+71 y\right] \geq 0$
$289+y^2-34 y-7 y+7 y^2+71-71 y \geq 0$
$8 y^2-112 y+360>0$
$y^2-14 y+45 \geq 0$
$(y-5)(y-9) \geq 0$
$y$ does not lie b/w $5 \& 9$