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Q.
The smallest integral value $c$ of $x$ such that $\frac{x-5}{x^2+5 x-14} >0$, satisfies
Complex Numbers and Quadratic Equations
Solution:
$\frac{x-5}{x^2+5 x-14}>0 \Rightarrow \frac{x-5}{x^2+7 x-2 x-14}>0 \Rightarrow \frac{x-5}{(x+7)(x-2)}>0$
$\Rightarrow \quad x \in(-7,2) \cup(5, \infty)$
Smallest integral value of $x=0=-6$
which is root of equation $c ^2+5 c -6=0$.
