roots of equation $ e^{2x}\sin (2x) +7=0$

Question

Let a,b,c be roots of equation $ e^{2x}\sin2x -7=0$ then roots of equation $ e^{2x}\sin2x +7=0$ lies between p and q where

1. Both p and q $\in$(a, b)

2. Both p and q $\in$(b, c)

3. p $\in $(a, b) and q $\in$(b, c)

4. p $\in $(a, b) and q $\notin$(b, c)

my attempt: I plotted graphs of $\sin2x$, $ e^{-2x}$, $-e^{-2x}$. But I have doubt further from here

Answer 1

Given the location of the roots (and assuming they are consecutive and $a<b<c$), you have $f(x)>0$ in $(a,b)$ and $f(x)<0$ in $(b,c)$, or conversely.

Now you are looking for the solutions of $f(x)=14$, which are both in $(a,b)$ or both in $(b,c)$ (you cannot tell).