Thank you for reporting, we will resolve it shortly
Q.
If $x$ is complex, the expression $\frac{x^{2}+34 x-71}{x^{2}+2 x-7}$ takes all values which lie in the interval $(a, b)$, find the values of $a$ and $b$
Here we have to find range of
$\frac{x^{2}+34 x-71}{x^{2}+2 x-7}=y$ (Let)
Then,
$x^{2}+34 x-71=x^{2} y+2 x y-7 y$
$\Rightarrow x^{2}(y-1)+x(2 y-34)+(71-7 y)=0$
As $x$ is complex, discriminant of above equation, $D \leq 0$
$\Rightarrow (2 y-34)^{2}-4(y-1)(71-7 y) \leq 0$
$\Rightarrow 5 \Rightarrow (a, b) \equiv(5,9)$