Answer
$c\in(-2,2)$
Work Step by Step
We are given the function:
$f(x)=\dfrac{x+1}{x^2+2cx+4}$
The function has domain $\mathbb{R}$ if the denominator is not zero.therefore it doesn't have real zeros.
Determine the values of $c$ for which the denominator is not zero:
$(2c)^2-4(1)(4)<0$
$4c^2-16<0$
$4(c^2-4)<0$
$c^2-4<0$
$c\in(-2,2)$
