Explanation

(c)
Let $y = \frac{x^{2} + 34x - 71}{x^{2} + 2x - 7}$
$\Rightarrow \ \ \ x^{2}(y - 1) + x(2y - 34) + 71 - 7y = 0$
Since, $x$ is complex number
$\therefore\ \ \ D < 0$
$\Rightarrow (2y - 34)^{2} - 4(y - 1)(71 - 7y) < 0$
$\Rightarrow \ \ (y - 17)^{2} - \left( 71y - 7y^{2} - 71 + 7y \right) < 0$
$\Rightarrow 8y^{2} - 112y + 360 < 0$
$\Rightarrow y^{2} - 14y + 45 < 0$
$\Rightarrow \ (y - 9)(y - 5) < 0$
$\Rightarrow \ \ 5 < y < 9$
$\therefore\ \ a = 5,\ b = 9$