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# Characteristic Equation of Complex Roots: Tangent Value of Zeros

DIFFEQ-LLNE5Y

Let $\phi(x)$ be the solution to the IVP (initial value problem):

$$y''+4y'+5y=0$$
$$y(0)=2$$
$$y'(0)=0$$

Suppose $\theta$ is one root of the equation $\phi(\theta)=0, \theta>0$. Then, the value of $\tan(\theta)$ is

A

$2$

B

$\cfrac{1}{2}$

C

$-\cfrac{1}{2}$

D

$-2$